 Make sure we're live and we are very nice, very nice. Hi everyone, this is Chichou, welcome to my channel and welcome to another live stream. Today is April 8th, 2020, fourth month, second decade, beginning of, and we're doing a live stream drop in math tutoring session for the 2020 school year, I guess, and this is number five that we're doing for this year. It's been an interesting year. There's a lot of people that are on lockdown, so schools have been canceled all over the place. Spider-Man, how are you doing? Catholic traditionalists, hello, hello, Chichou, good afternoon, friends, hope you're well. Good evening, good, good folks, good evening, good evening. Welcome, welcome. I've been looking to this stream, I'm just curious to see what we're gonna get. I, we had a question from someone, Olive, she's in Norway I believe, she needed some help with calculus and because they're nine hours ahead, I thought maybe I would do a little intro on calculus. Connor, how are you doing? A little intro on calculus is what I know works, how's life. Maybe, we'll see. I looked at it for like 15 minutes. I brought out my book, my calculus book, and it just did one problem. So maybe if we get a chance. Hannah, how are you doing? Hey Chichou, I'm nesting in bed, chilling with you Chichou. Awesome, awesome, nice, fun, fun. And I'll do my little intro, the focus is going in and out, it's like spring, summer hot right now, so the the cameras sometimes is getting cloudy and bright and stuff like this. But as you know, technique, how are you doing? Hey Chichou, how's quarantine treating you? Not bad, I'm eating. I added one more thing to my repertoire of apple sauce and my coconut flour, whole wheat, coconut whole wheat flour, honey, chocolate chip, walnut cookies and apple sauce, homemade apple sauce, I added mandrons in there. So these are cookies that I made, right? And this is apple sauce that I made and these are some mandrons, right? And the cookies are really crumbly, so I've been munching away cooking and eating BDS, how do you, how should I pronounce your name? B-D-E-S-S, BDS, no idea. Good evening, good evening. Quinn, how's life? Hey Chichou, how's it going? I made another stream once again, so I said awesome, awesome, and a math stream, math stream, math stream. I'm loving the math right now, just because I'm doing a fair bit of mathematics online and I'm getting really powerful students that want to learn as fast as they can, so I'm going rapid mode, right? Just feeding them as much as I can because they're not in classes, right? So they're not being dumbed down, right? So when they're in classes, most kids, they get dumbed down a lot, right? The class goes so slow, they get bored out of their minds, they think mathematics is boring, they can't pay attention. Now that they're not in classes, I'm teaching them directly what they need to learn and I'm going rapid, right? And they're just sucking it all up. That's the way our education system should be, but it's not. So I'm really appreciating this opportunity to feed as many people as possible. BDS, life day in the show, BDS. Okay, BDS. Boycott, divestment, sanctions. I'm clearing the house, I'm clearing the house, excited to listen to some math. I'll be in and out of chat. Your streams make me super motivated to clean. Awesome. That's good. 11 30 a.m. for me in New Zealand right on, right now. What time is it for you? For me, it's 4 30 p.m. So you're a day ahead, right? So you guys are 18 hours ahead. Is that true? Dark, dark, ruler with, how are you doing? Looks delicious. Might have a hand at cooking during this. Cool. It's really good. Like with the applesauce is amazing. Like I mix it up because a coconut makes it dry and popping on an orange. So the mix is amazing, right? And it's got chocolate, dark chocolate in there too. So super yummy. Come back to vouch for that, Chico. Hey, Chico. Hello VC, how are you doing? Dragon. So Chico, what's up chat? This is the ninth of April. Yeah. So you guys are 18 hours ahead. New Zealand. Cool. I sent, when I was selling some comic books on eBay, I had one person buy a whole bunch of comics on eBay and we held off until we could send them a package. Wow. It cost a lot of money to send those comics to New Zealand. Huge. I'll always be making it. I'm a teacher, but I have even less participation than I did the first week. I said a few weeks ago, I was afraid it is too late for them to get excited about learning. I wish I knew how to excite people better than they are now. It always be making. It's going to take time. Seriously, brother, you should see how long it took me. I've been at this for 20 years, right? Man, it took time. And it's word of mouth that goes out, right? Like when I moved to this new city, I still kept my students from the other city. So for the first two years I came here, I was going back every week like exhausting, cost me money, exhausting, but I couldn't let go of the students, right? And slowly, I've been here like seven years now, I guess. So word of mouth has gotten out where, oh, you get chicho, you get chicho, you teach mouth, you get chicho. So all of a sudden there's a, it's almost exponential. At some point I won't be able to take the capacity anymore, right? So right now I'm trying to fill as many, help out as many people as possible, fill in as many spots as possible, right? Because people need the help. But I'm lucky to a certain degree, always be making. I, like, I have students from all spectrums, right? I don't have students, well I do that. No, I can't say. I have students from all spectrums, right? So I can mix it up. And I do one-on-one. It's a different, different thing or two-on, one-on-two and stuff like this. It's a different thing than trying to motivate 30 kids in a classroom. Virtually impossible. And you can't sustain that for extended periods of time. Martin, how are you doing? I'm here. I'm awake. Martin, crack me up. For those of you who don't want to know, this camera is going to zoom in on that. For those of you that want to know, Martin's in the UK. So they're eight hours ahead, right? So it's one time is at 1.30 in the morning. Awesome. I hope, I hope the action yesterday with the gloves and the lotion went well. What a while of Martin. Good. Okay. Hey everybody. Will show, how are you doing? Gicho has no limits. Well, he can't afford, afford to know them. It's a big pain shipping things into these huge, oh my God. My mom has a business where she ships things from China and it is a big expense of making everything here more. Yeah. It was, it was crazy. I was like, how much? Wow. I've been streaming every weekend, but I have one student, student viewer out of 140. I thought my relationships were, don't do it on the weekends. Always be making, not on the weekends, right? I do streams on the weekends because that's when I can fill them in, right? Do it on a weekday. For some reason, a lot of students, they think weekends are break time. They don't, they don't want to do schoolwork, learn anything on the weekends. They're out to play. So they're already programmed into the slave lifestyle of working nine to five and partying on the weekends, right? So if they're already programmed and not the brainwashed, indoctrinated into that system, work with them on that system right now as much as you can. For me, when I work with my students, I make me available on the times and days that they want me to be available. I don't go with my schedule. I go with, I go with, I go with their schedule. I have to because I'm trying to teach them math. I'll do whatever it takes to teach them, right? So I go with their schedule. That's why if you go to on my Discord and Patreon and you, like, I've set this from the beginning. When I say, okay, what do you guys want to stream? What do you guys want to do? I say, just let me know when and I'll try to make myself available during those days and times, right? So when you're doing it this way, you have to be flexible on them. Okay. So it's sort of very shift work style of doing this. Yes, very well. It went well, Martin. Nice. Nice. Nice. I won't go deep into it. Hello, Mr. Hello, Wolf. How are you doing? Intracoi. Hi, hi, hi. I'm exhausted today. Oh, oh, that's good. If you're exhausted, I hope it's extra clicker activity. Good afternoon. Isolation day 15 here. Yeah. For me, it's sort of, they haven't really locked us down, but they suggested. So like, I'm barely leaving the house. I haven't left the house for, I don't know, four or five days. And the only time I leave the house is to go for a walk. And I go for a walk and I come back. It's a two hour gig, right? Good afternoon. I said weekday. Oh, weekday. Okay, weekday. Well, maybe stream on the weekends. Ask them when they're available. Is this stream suitable for me if I don't know math? For sure, Wolf. For sure. Keep it secret. Keep it safe. Keep it secret. Keep it safe. I went on a 30 mile bike ride through Manhattan, Brooklyn. Nice dragons. Awesome. New York. I know I shouldn't do that, but the streets were vacant. Cool. As long as you're keeping your physical distance, safe distance from people, why not? Right? And by the way, again, we're on Patreon. Okay. So if you want to follow us, Patreon is a good way to be, you know, good place to check out. And if you want to support this work, Patreon is a great way to support this work. Okay. We are, for those that are watching this on another platform, we are live streaming this on Twitch. So if you want to catch these live Twitch is where you want to be at. Okay. I do announce these streams on Twitter, Mines, Gaps, VK and Elo. Those are social platforms I'm on. I will try to follow. Cool. And oh, Spiderman. Thank you very much. And we do upload these on YouTube and Bitshoot. Okay. Everything goes on Bitshoot. Almost everything is going on YouTube right now. Everything is going on YouTube right now. We'll see where that goes once YouTube filters and sensors go into hardcore production mode, right? Hardcore production mode, because they are going into hardcore production mode, right? So hopefully we'll be okay there. And if you're on YouTube, we just got authorized for YouTube channel membership. Okay. So you can join YouTube. That's a good way to support this project as well, as well as joining on Twitch through tier one or Amazon Prime and stuff like this, because Amazon Prime doesn't ding you, dings Amazon, which is a beautiful, beautiful thing, right? And flatten the curve game. It is important. It is important. Okay. Don't overwhelm your healthcare system because that's the line that you see here that you see here. That line right there. That's the capacity that your healthcare system wherever you live can take. So some places their healthcare systems are really good. So they can take a heavier load. Some places not so much, right? Depending on where you are, make sure you're in the gray zone where your healthcare providers can, you know, they're not overwhelmed. They can take care of everyone. Okay. You don't want to be in the red zone and the red zone, it means not enough bed, not enough nurses, not enough equipment, not enough doctors. You're going to be waiting in line to have access to healthcare providers. And if they don't get to you fast enough, might, uh, might be time to check out. You don't want to push it to that level. Right? So take care. Okay. Be aware. Aside from that, let's do a little mathematics. Boop. Evening to Joe, intelligent blueberry. How are you doing? Here in New Zealand, we're on full lockdown. Uh, we're only allowed going on walks and going into town to get food. We only have around 1000 cases and one that that's good, Quinn. We're doing a relatively good job compared to other countries. Yeah, that's fantastic. Really. It's just delaying it until, because we really don't know what this is. Right? So you just want to delay it until you figure out what the hell's going on. I meant to join, but I don't know which level yet. Oh, Martin, take your time, brother. I'm going to be around for a long time. And thank you. Thank you for wanting to join. Okay. I'll always be making, I'll save my questions for the education stream we're doing. So yeah, let's talk about education then. Let's focus on mathematics right now, but just be warned. I'm going to be doing a lot of chatting. Okay. Would it help if I submitted my questions ahead of time? Always be making. Yeah, post them on discord because there might be people that might not be able to go on the live stream that want to participate in the discussion. So post your questions on discord or your concerns and your thoughts on discord in the education folder. I'm pretty sure we have one. And uh, slowly we'll tackle it, right? Because this might be a long term thing. People were outside today in, in park in my area, at least 30 people and groups of six plus together, close proximity more. That's just silliness. Right? Irrelevant of what people think this is, if it's real or not real, if it's really contagious or not contagious, be respectful because the people around you are your community, right? So if they're your community, you don't want to make people anxious and stress them out and induce fear into your community. Because once you induce fear into community, it takes a while for it to dissipate and you don't want to be the dangling, standing out saying, what a moron that guy is. Right? Am I allowed to say that on Twitch? I don't even know anymore. It's silly. You know, irrelevant of what you think it is, right? Here in New Zealand, we have done more than flatten the curve. We're going, going down in additionally confirmed cases compared to previous days. Awesome. That's good. Well, thank you for taking the business. Is it possible to do physics problems during a math stream, even if algebra is for sure VC? Yeah. My background is geophysics. By the way, I'm really rusty on my physics. I know my mathematics more, but what do you think would happen to those countries that don't consider quarantine? Well, we're seeing Sweden. We were talking about the looking at the data out of Sweden, right? Because they were taking the, uh, taking the measure of les affaires and let it be, see where it goes. And it looks like their numbers are increasing hardcore. So it looks like they're going to induce, uh, suggest, uh, more tighter measures. Okay. Martin, thank you. Nick less. How are you doing? Hey Chico. What's up bro? Doing good brother doing good. Ma's no mercy, no mercy. Yeah. It's not worth it anymore. Right. Um, it's, it, I'm okay with mercy. I'm okay with people who are just playing and stuff like this, but right now it's a little tight right now. The situation is, is heavy, right? So the trolls being heavy, they're, they're the ones that need a little smacking around, right? Not literally violence never solves anything. Dragons. Yeah. There are those mass gatherings for funerals of figures who died of coronavirus. Just don't get it. I don't get it. I don't get it either. It's crazy. You should be able to say whatever you want onto it. Really. Uh, you should be able to say whatever you want anywhere. Really. As far as I'm concerned, right? Um, what then reason? I mean, don't go into it, but don't go into a church and say, I am Satan. You could if you want, but what are you an idiot? So you can be an idiot and they're allowed to throw you out, but it's, it's ridiculous. Censorship is absurd, right? Josie, uh, should do some more, um, asteroid problems turns out they can boil some water. By the way, we did a huge asteroid problem for one mass stream trying to figure out how much of Lake Erie we would evaporate and stuff like this. And we figured out it was multiple Lake Erie's. It was a devastating, it was amazing. Super fun. Catholic traditionalist. I like the idea of posting questions to discord. I would love to participate in the education discussion, but it might not be online on Friday since it is good Friday. Yeah. Catholic traditions. Exactly. Like that's one reason the discord has turned out to be amazing where we are. And you can find the link on our Twitch page and the description of this video on YouTube and bitchy that has loaded on, right? And there's the links and all the other platforms I'm on. Amazing discussions taking place, right? I've been waiting wanting to get a degree in video game development and mathematics is the core of designing and programming games. So these streams make me dream, make my dream come close. Awesome. Spider-Man. So what math are you planning on doing today? Quinn, high school math, open question, almost whatever you want. I reviewed for like 15 minutes to calculus question that all have had on the previous stream. She wanted to know. So I can do a little quick calculus introduction, but I'm just waiting to see if there's any, any important, any urgent questions that people have right now regarding math, because I know people are studying from home and they're, they're, they're students that are concerned about their grades and the content because they need to know this material before they move on to the next year. Right. So if there's any questions on math coming up, I mean, we're about 20 minutes into this. So I might do the calculus right away because we haven't, no, no math questions have come up yet. The trolls in this chat seem to be different from garden variety, a twist trolls. They're just strange. There's a few strange ones. I'm a qualified door supervisor. Violence is the last resort, but sometimes, sometimes, sometimes, and it's not, unfortunately, the, the confrontation, physical confrontation, it's not going toe-to-toe with them. It's submission. If the situation, just keep this in mind again, if the situation ever arises where there's physical confrontation happening, you don't want to go to toe-to-toe with anyone to see who causes more damage on the other person and stuff like this. You're going into submission. Right. That's why wrestling and jujutsu are two of the best self-protection courses, training that you can take because most physical confrontations don't last more than 10 seconds. Okay. If you're smart about it and the one who can submit the other person is over. Grapple done. Like really, three seconds, it's over. Okay. Isn't glass a verb where you're a glass, glass? I don't know. You've got to be vigilant, vigilant. Did you hear the breaking news burning? Yeah, for sure. Tested negative. If you don't mind me asking, what's your ethnicity? I am asking because you look familiar. System of a down. Search. Thank you. I'm Armenian blood born in Iran, West Coast Canadian. I'm West Coast Canadian mentality. Yes, it's a dangerous area. I live in. Yeah. Yeah, Martin. I'm pretty sure companies like YouTube and Twitch aren't legally liable for the comments that are made on their websites, meaning they're the phone company, not the publication. So they have no bias where they need to censor anything. When they censor up the yin-yang, a YouTube more than Twitch so far, right? But Google, oh my God, they censor up the yin-yang, right? That's why I use most of my searches are through go, not Google, right? One last night, one plus one, sometimes equals one. Sometimes it was one. Sometimes they cancel each other out as zero, right? OK, Chicho, can you teach me how quadratics work? I somewhat understand how to find the equation. And what not? But I am super confused with how it exactly works. Sure, Quinn, Akido and Kung Fu for me. OK, Akido, Kung Fu, cool basis. Oh, boy. Mask of Raven. Yeah. They shouldn't have to. Mask of Raven. How are you doing? Quadratics, we've done a lot by the way, Quinn. If you do a search for Chicho quadratics, you'll find it. OK, so I can do a speedy Gonzalez version for you just to explain to you what it is. It'll take five minutes because there's a lot of people who have been on the previous live streams. They seem to quadratics play out multiple times, right? Chicho glass for glasses in action. Is it often? How are you doing? How do you show hope all as well? That explains I am Kurdish born in Turkey. Awesome. My father speaks Turkish, by the way. My point is they have no valid reason for they have no valid reasons for doing it. Of course not. But it's control mechanism, right? Twitch wants to lure advertisers so they censor content. I don't think it's just about advertisers. It's about control. OK, when Google bought YouTube, I lost all hope. Yeah, not that they aren't doing it. OK, OK, found Tokyo goes from a seller here in Sweden. Looking forward to the shipment. Awesome. Also, my wife loves the 10 by 10 puzzle you showed in your videos. Also, peace, brother. Good to see you. Awesome, Nikki. Awesome. Awesome on all parts, by the way. Tokyo goes, I hope you love it and 10 by 10. What a meditative game. Would you be able to show us some matrix vector up? Oh, I haven't done it. I'm really good at it. I used to, I ace the whole thing, like 98 percent at university. And I taught it to myself and have an amazing book that teaches it. But I forgot how to do the determinants and matrices. I would have to do a review on it. OK, really, Tokyo goes this great. Sean Murphy's art is a beautiful art, beautiful art. When I have the opportunity, Dolphin, I'll review that material. But before we get into this, let me deal with the quadratic. It's going to take five minutes. For those of you who've seen this, you won't get a little snack break. Five minutes, I'll be done. And then I'm going to show you guys an intro to calculus. OK, I just did a little review for 15 minutes. I got the time and I did a little review and I'm going to do this. So we'll I'll post a message to all of them on our disco. And just say, watch this segment. Hopefully it'll help her out. OK. But here's what quadratics are. Quadratics are functions that are extra power of two. Basically, the polynomials of the form f of x is equal to let's call it a1 x to the power of n plus a2 x to the power of n minus one all the way down to a constant c. OK. Now, quadratic, sorry, polynomials, these are polynomials. OK, where a1, a2, all the way down to c, they're all just constants, they're numbers. OK, x is just your variable. And n has to be n is the element of the natural numbers. Right. So n can be positive whole numbers, counting numbers. Quadratics are the ones where x is to the power of two. So if it's x to the power of two. OK, let's call it a1 x to the power of two. The next level down would be a2 x to the power of two minus one, which is one, plus x to the power of zero, which is just a constant, which would be a3 x to the power of zero. But x to the power of zero is one. Anything to the power of zero one is one. So it's a3 and a3, which is called a constant in general. Right. It's just a number. OK. So quadratic is a function that is x to the power of two. You don't need this. You don't need the constant. So it could be just x to the power of two with a number in front. It could be x to the power of two plus x to the power of one. Or it could be x to the power of two plus a constant. Or it could be x to the power of two plus x to the power of one plus a constant. OK, that's what a quadratic is. So, Chico, imagine there are two horses in a triangle for you. Oh, that's so weird. We did that problem last stream, or a couple of streams ago. OK, so this is what a quadratic is. Visually, this is what a quadratic is. A quadratic either opens up or opens down. It's a curve. It's a parabola. It's the trajectory of a pen. Watch this. Hopefully I can catch it and not make noise. That is a parabola. OK, so this thing could look like this or look like this. Right. And there are different versions, different functions give you each one. Right. And guess what? Quadratics are made up of two lines multiplied together. Right. So, for example, let me give you an example. I don't know. I think that's easier to use. Why instead of f of x at this level? Students don't understand the true meaning of f of x. F of x is y. Right. F of x is y. That's it. Right. I know a lot of people have a hard time with f of x. F of x means y. This doesn't mean f times x. It means f of x. The one thing. Yeah. I'm my age group for this. We use y. Let's use y. OK. But get used to f of x. It's a better, better presentation of a function. OK. Let's call it y. So, for example, let's assume you have the following function. y is equal to x plus 2. And you have, so that's y 1. That's one function. And then you have y 2 is equal to let's go 3x minus 1. Right. If you're studying quadratic, you know how to graph lines. So we're going to graph lines. This guy is 2. Slope is 1 over 1. So that's that line. This guy is negative 1. Slope is 3 over 1. 1, 2, 3, 1. That's that line. So, hey, let's create a new function. That's what we do in mathematics. We take one function here, one function there. Put them together. What do we got? Right. So let's create two functions. I'm going to create a new function. I'm going to call it. What do you want to call it? F of x. Right. And F of x makes it much easier to refer to y at a given x. Yeah. Right. So what are we going to call the new function? What should we call it? h w z. You'll see it in more advanced functions in the future, like the inverse function. In Toronto, you will see that in grade 11. Yeah. In grade 11 and in grade 10 in Vancouver, in BC anyway. Right. So let's create a new function. Let's call it y3. What kind of function are we going to create? Oh, we're going to multiply y1 times y2. y1 times y2. Well, y1 is x plus 2 and y2 is 3x minus 1. Okay. So y3 is x plus 2 times 3x minus 1. Okay. Cool. So what are we doing here? We're going to create a new function that is this function times that function, which is this line times this line. So we're going to visually, we're going to create a new function, which is a line times another line. Okay. That's what a quadratic is if we're creating it. Right. So this becomes, foil the sucker out. You get 3x squared minus x plus 6x minus 2, which is equal to 3x squared plus 5x minus 2. Here's y3. Right. That's our quadratic function. Guess what? What does the graph of this look like? The graph of this looks like this. What? We just multiply two lines. I got this. Right. That's what you're studying. Quadratics are the next level above lines. Why are we studying quadratics? Because most polynomials, all polynomials, all polynomials. Right. And a polynomial or something like this. This is a polynomial. Right. That's a polynomial function. So this is what it looks like written out. Here's an example of a polynomial function. Right. Example of polynomial function. Visual. Here's a polynomial function. That's a polynomial function. Well, guess what? This function is made up of lines multiplied together. So these are lines you can think of them as prime factors. Right. So for example, if you have 6, you're going to break down 6. 6 breaks down into 2 times 3. Right. So 6, the building blocks of 6 are the two prime numbers 2 and 3. The building blocks of this function are x plus 2 and 3x minus 1. Okay. The building blocks of this function is going to be 1, 2, 3, 4, 5, 6, 7. At least 7 lines multiplied together. Okay. That's what it is. Now, before we go into studying polynomials and 7 lines multiplied together, this would be x to the power of 7. y is equal to a coefficient, a number in front, x to the power of 7 because it changes direction 7 times. That tells you what the power is. This is changing direction twice. So it's x squared, x to the power of 7 plus the rest of it. Okay. Based on the definition of a polynomial. So the reason you're studying quadratic functions is to kick yourself up to be able to appreciate, understand more complicated functions in the future. That being said, there's a lot of stuff that follows the principles of a quadratic function. So that's why you're studying this. And basically, quadratics are two lines multiplied together. As for how to graph these things, how to find the vertex of this thing, the axis of symmetry and stuff like this, do a search for Qichu quadratic functions, completing the square. Just type in here. I'm going to erase these. Type in our search. We got at least four or five videos on this. Probably more six or seven or eight. I did a whole series, language of mathematics, graffiti style on the walls, going out in the city doing big chalk and some of the stuff cutting it to rap music, right? Like doing mathematics, right? Look for Qichu completing the square. Do a search for Qichu completing the square. It'll show you how to graph these things. Okay, I hope that's okay. There's a lot of chat going on. If you go on to learn calculus, this will all make sense. Yeah, what I'm going to do right now is I'm going to do a little intro for calculus. Okay, if that's cool. Grade 10, what age is grade 10? 15? I don't recall doing this at school. I don't remember doing this at school, but for sure you guys did it. 15 or 16, yeah, okay? So next year for me, next year for you probably quit. Important, okay? If you go on to learn calculus, this will all make sense, right? It's like a cheat code to mathematics. Calculus is when I really found my love for math. Some problems you need to imagine. Yeah, two imaginary lines. Like over here, you would have a couple of imaginary lines multiplied together somewhere. Okay, most likely. Quadratics are very useful for basic physics problems. Yeah, parabolas, projectiles. There are all the gamings. Like all games, really, they have physics in them, and they all have quadratics in them. The functions that they follow, right? Because it's just gravity. They have to introduce the concept of gravity in there. They're very useful for basic physics problems. Those are very useful when you understand how to drive equations from certain problems. Yeah, and we've done a few of those, driving the quadratic equation of the function. Yeah, that would make tons of sense for physics, yes. How is this math used in the world? How is this used in the real world? It could be maximizing revenue. And if you do Chichou maximizing revenue, completing the square, and do a search for maximizing revenue. We did a maximizing revenue. I believe it's one of the problems we did for personal finance or economics where I was trying to maximize revenue selling firecrackers to other students in high school. I didn't know it was completing the square back then, but we did it after the fact. Keep in mind it doesn't have to change seven times. Oh yeah, yeah, that's right. The thingamajigis on it. If that's what you mean, mask over here. The next one could be x cubed plus two. Well, that wouldn't graph that, but there's nuances involved with it. That's right, important to keep that in mind. Yes, yes. Here's that. Oh, awesome, Spider-Man. Thank you very much. Swiss 59. How are you doing? I turned 15 in five days. Nice. Happy birthday, Quinn. In general, quadratics are useful to know for logarithmic functions, which are the inverse of an exponential function. Yeah, and basically what Iron Smash is talking about is this. It's not quadratic. Well, it is, I guess. But it's exponential, right? Because logarithmic functions are this. That's an exponential, and a logarithmic does this to it, right? Or, yeah, basically. Wait, I remember that now. My call of duty is a Q base. In engineering, I have a problem that combines calculus, quadratic equations, and complex numbers all in one. It was so cool seeing things come together like that. Yeah, I wish that we're doing this. They taught this in high school, right? Money, yes, money. Maximizing, oh, Spider-Man, you rock. I posted an essay in the Education Folder Discord that I would really appreciate your input on in the education stream on April. Okay, I'll always be making. Is it really long? I hope you got a condensed version, brother. I'm going full speed right now, right? So my time is very condensed, because I have to stay up with the politics and economics, right? That is a passion that I have. Okay, so all the other articles that are very extended, if you can do, it's like a page. Oh, yeah, that's okay. Page is good. Page is good. Happy quarantine birthday. Happy quarantine birthday. Not to minimize any younger viewers, but seeing this now is extremely basic when you have done more complicated functions. Go on to learn math. It will help day to day. 100%. Iron Mountain Smash. 100%. I mean, just imagine, if you're in high school right now, right? Let's say you're in grade 10, okay? If you think things are difficult right now, just think back two years in grade eight. There was mathematics you were trying to learn that was considered that you would have considered, oh, this is really difficult. I'll never learn it. And now that we look back on it two years ago, you're like, oh man, that is so easy. And you see people struggling with it. You're like, what are you guys, dum-dums? That is so easy. But remember, you used to think that was hard, right? So whatever you're encountering right now in mathematics that you think is hard, it's not hard. It's just new. You just have to put the time and the effort in to learn it, okay? Ridiculously important. And if you go into every, every bit of knowledge, information that you encounter with the same mindset, congratulations, you're a free human being, right? That is what you need to do. You need to be proactive in your education. Don't be a passive consumer of information. Be active, right? Spider-Man is the link king. Very much appreciated Spider-Man, by the way. Did you ever study statistics? Oh yeah, for sure. T-distribution standard. Oh, for sure, for sure. I took stats all the way to third year. I don't, and I used to teach it in high school, but they took it out of the curriculum. I was pissed, right? Because I love stats, but I haven't taught it on a full-time basis for like 15 years. They took it out 15 years ago, so I'm not as powerful. I have to relearn a lot of statistics, but the Z-distribution and standard deviation and variation, linear regression, I used to do a lot of that stuff for geophysics as well in the 1990s, right? When I was working as geophysicist. Most of the benefits from math for me isn't because I use calculus daily, but just the way of looking at problems, yeah. Just the way of looking at the world, as Mask of Raven says, every language you learn in your life gives you a different perspective so you can understand things a little differently, right? Look at problems in a different light, and sometimes shining a light on a problem in this angle makes it obvious, right? I believe it's Robert Anton Wilson that I don't know if this is true or not. He said basically it's easier to understand relativity, Einstein's theory of electrodynamics of moving bodies in Swahili than it is in English. Now, I don't know if that's true or not, but I speak three languages, and there are certain concepts that are easier to understand in the different language. Now, just imagine if you learn the universal language, right? The language that defines the universe, which is mathematics. Just imagine how much power you would have if you tried to understand the world. Wow, wow, wow, congratulations. You just became a free human being, right? My theory is they remove stuff from the curriculum to dumb people down, right? I use math this morning. False stock, take, and profit margin for last quarter. Nice. What are we working on right now? I don't know. Right now I'm going to do a little intro to calculus. Okay, that's it. Feynman techniques. If you want to know your level of understanding, teach it to a five-year-old. If you can't, you don't understand it well enough. This is a great way to master subjects. Teach it to others, teach it to others. Thank you very much, Muraly Human. My mathematics became powerful when I started teaching mathematics. Not when I was studying mathematics, getting a math minor, getting my geophysics degree, doing geophysics for 10 years. My math became powerful when I started teaching it because students would ask me questions and I didn't know the answer to, so I'll have to look it up. Transmission is the ultimate code of learning. Transmission is the ultimate mode of learning. Good point. I'm an engineer and I can attest that I use calculus, linear, algebra, differential, all the time on an almost daily basis. Okay, I'm going to scroll down just to make sure there's no math question before we jump into the calculus. If there is, for reference, 78% profit margin. 78% profit margin. That's good, Martin. That's good. Too complicated for me. So far, I've been good without using it. Everyone's different, I guess. El Homiro? But I have heard a lot of people benefit from it. What are you, just mathematics in general or calculus? Calculus I don't use in my daily life, but the understanding of calculus, what it represents, I use every day in my life, which is the concept of change, rate of change, how things change, the introduction of time into calculus, into mathematics. That's the way I look at it. They took stuff out of the curriculum in here, but we still have the option to take the test and get the extra credits and stuff just that our teachers won't teach us. Yeah, and slowly they'll disappear, right? I'm very unfortunate. Very awesome. I always consider engineering. I'm going on to become a biochemist, cool. So unfortunately my major is slowly starting away from math. If you go far enough, I'm pretty sure it's going to clink back onto math. Another 5K from my portfolio. Nah, it's Martin. If a teacher will not teach it to you, see if you can find someone else to teach you or teach it to yourself. You can call me Gio. Gio, nice. But Gio isn't... If I don't remember Gio, let me know again. Slowly I'll remember. Let's do a little intro to calculus. And let me see what time we're on. We're about 45 minutes in. And I'm going to do the intro that I know to calculus. I just did a 15-minute review of it. The book that I have... Thank you very much, Dolphin. The book that I have, which is this guy. This is my to-go-to book. I got this at university and this is the book that taught me calculus. I didn't have a teacher teaching me calculus. I took calculus. I had professors that taught me calculus but I didn't learn calculus from them. I learned calculus by reading this book. This is my to-go-to book. One of the most precious books I have in my collection because I use it the most. I spent many hours on this book. I went to the part where it shows you the fundamental theorem of calculus. I think I'm calling it fundamental theorem of calculus. I'm going to give you a visual of what calculus allows you to do at a very basic rudimentary level. Mask of Raven and there's a couple of other people here that know calculus well. If I make a mistake, I'm going to keep my eye on the chat because I just did a 15-minute review. If I make a mistake, let me know so I can correct it. People that are going to watch this, specifically Olive, if you're watching this, you won't get false information from me. Is this meant for a specific person? Because quadratics to calculus is a jump, I say. Well, quadratics to calculus, to a certain degree, but we could use quadratics to talk about the calculus. I think quadratics was a review segment. Calculus is the main content, I think. I'm trying to. Because I know the person that requested this lives in Norway and they're nine hours ahead. I don't have another math stream lined up for another two weeks at least. So I think they needed help with their class. So the best I could do is just review quickly. In your experience, what is one thing that makes people struggle with calculus? The way it's taught. Really, the way it's taught. That's it. And understanding fractions. You have to understand fractions. Limits and stuff like this. But it just goes down to the way it's taught. Bad teachers, bad system. No, really, yeah, really. Mathematics, the reason why people struggle with mathematics is because it's taught poorly, period. That's the only reason. And why is it taught poorly? Because of centralized education. So it controls the curriculums. Never been great at math, but I respect it and I recognize it's important. It's super awesome that you're doing it. Yeah, we have to. We have to. And not knowing function as well. Yeah, anxiety, yeah. But that's a reflection, sort of byproduct of our education system. That's so correct. Availability. When the teacher isn't interested in teaching, it's hard to be interested in learning. Anything can be taught if taught well. Yeah, 100%. Calculus. Let me give you a little intro on calculus. Now, one of the reasons we do mathematics is to try to understand the world around us. Right? And one way we try to understand the world around us is to come up with functions that explain different systems. Okay? And functions are basically you can get, you know, something, a function. Here, this is a function. Y is equal to 2x squared plus 5x minus 1. That's a function. It's a parabola. It graphs a parabola. Here, let me make this simpler so we can graph it so you can see exactly what it would look like. So let's assume you had plus 6. So if you're going to graph this function, this function if you can factor it x plus 2 x plus 3. And what you can do with this function is set y is equal to 0. Let me make a little bit of more room. Let me give you a little bit more info. Right? So if you factor this function it's a quadratic function. You get this. And one thing you want to do with functions is be able to graph them. Right? So what you can do is draw your Cartesian corner system, x and y and go, hey, I want to graph this. How can I graph this? You can create a table of values. And plug in numbers for x, figure out what y is, or plug in numbers for y and figure out what x is. Right? So what we're going to do right now is we're going to plug in numbers and number for y and figure out what the x will be when y is a certain number. And for us, what we're going to do right now is we're going to plug in 0 for y. Right? So let's do this. x and y. Let's create a table of values. We're going to plug in 0 for y. And we're going to try to figure out what y is. Now we can plug it in this part and go 0 is equal to x squared plus 5x plus 6. Right? So we got x squared plus 5x plus 6 is equal to 0. Remember, that's your y that I just substituted for 0. It doesn't make a difference if I put the equal sign here or equal sign here. I like my 0, the equal sign to be on the other side when I'm trying to solve equations. Right? So if we're going to solve this, we're going to factor it. x plus 2, x plus 3, and the power of 0, and we'll have a video out that says, you know, what's the power of 0? One thing that 0 allows you to do is, if you have two things or more things, multiply together to give you 0, you can set each one equal to 0. So you can go x plus 2 is equal to 0. x plus 3 is equal to 0. So x is equal to negative 2 and x is equal to negative 3. What did we just find out? What did we just find out? We just found out what x can be when y is 0. So if we set y as 0, then x can be negative 2 or negative 3. What does that mean? That means we just found 2 points on this function, on this graph. Right? So when x is negative 2, y is 0. When x is negative 3, y is 0. So we can put these 2 points on the graph. Right? Let's go. Here's negative 1. Here's negative 2. Here's negative 3. So negative 2 and 0. Negative 3 and 0. Those are 2 points on the graph. Right? Cool. So when y is 0, x can be negative 2. And when x is negative 3, y again can be 0. Well, what does that tell us? That tells us this graph is not a line, unless it goes like this and we know it's not. Well, we know this thing is a function. And because of the way it's written, we know it's a parabola and it looks like this. Right? And the way it looks, there's an axis of symmetry here. So we know that the function goes like this. Right? Because the number up here is positive. Okay? Now we need more than 2 points to be able to graph a parabola. So what we can do is just plug in another point. Let's say plug in the middle point here. X is negative 2.5. Right? Because no one says we have to just plug in values for y. We can plug in x is equal to negative 2.5. Let's see what happens between these 2 points when x is negative 2.5. If we plug negative 2.5, we can plug it into the original one or we can plug it into the factored version. Right? So what I'm going to do and you wouldn't erase any of this. Right? If you're doing the work trying to graph something, don't erase it. But we got limited space. I'm going to erase. Okay? So what I'm going to do is I'm going to say okay, I'm going to take the original function y is equal to this and I'm going to factor it. I don't want to plug in negative 2.5 for x. I'll find out what the y is. Right? Negative 2.5 plus 2 negative 2.5 plus 3. Right? Negative 2.5 plus 2 is negative 0.5 negative 0.5 negative 2.5 plus 3 is 0.5 0.5. Right? 0.5 times 0.5 is 0.25 and a negative times a positive is negative. Right? So this is negative 0.25. Now I'm going through the speedy Gonzales because I want to get to the calculus. Right? So I'm just giving you a basic function that we're going to look at. Okay? So all of a sudden when x is negative 2.5 y is negative 0.25 and Chad, if I'm making any calculation problems, please let me know. Right? So all of a sudden we got this. If this is negative 1 here, when x is negative 2.5, y is negative 0.25 which is about here. So this graph comes down like this and goes back off and shoots up. Okay? So we just graphed quadratic function. The number is on the half. Happy face is that what it is? Right? So we just graphed quadratic function. Now what does calculus do? Okay? Let me erase all this. Now keep this graph in mind. I'm going to make it bigger. Okay? I'm going to kill these guys too. Because what we want to do is take a close look at this thing. So we got this guy so far. Negative 1, negative 2, negative 3, negative 1, 1, let's put a scale there. So we had this and here and the graph goes like this. Does that look like a parabola? Let me draw a little bit better. My parabola sucks. So much more interesting when I'm not learning for a grade. Yeah, for sure. Right, big witty? Crazy. A grade? What is a grade? You're learning for the sake of learning and doing. Take a look at that. Well, this was an easy function to graph. This is what calculus allows us to do. Calculus says this. Let me bring a different color pen. Let's see if our red is okay. Oh no, there's, you can't tell the difference between those guys. Let me do a green. Let's bring out a green. I don't want to make too much noise, the mic is right beside it. Is that dark enough? That's not dark enough. Purple? Purple? Purple. We're going to go with purple. Purple, purple. Okay, take a look at this. Calculus allows us to do this, right? When we're trying to understand functions. This is a simple function. This is very predictable. You can see where it goes. It just goes on forever. This is very predictable. It just goes on forever. And it comes down and it does a little turn and we found the point. Now just imagine if you had a more complicated function. You were given an equation or you were given a visual, a graph, and you're trying to find the exact points where things change up. So let's assume we had a function. Let's assume we had this guy. Something like this. Now there would be a written format of this. An expression representing this function. That graph would work great for my creating and put out the equation. So you would have a function like this that represents this. And in the real world, right, when you're taking mathematics and when you're trying to apply the mathematics to the system, when you're trying to understand the system, the system is predictable if it's going like this. There isn't really anything going on. in this direction at a given magnitude. What is important for functions is when they change directions. When they go in another way, when the momentum changes. So for example, take a look at this. What are the important points of this function? Think about this. What are the important points of this function? Well the important points are one of them would be one of them would be the y-intercept, where it crosses the y-axis. Right? Another one would be where it crosses the x-axis. So for this guy we found the x-axis. That's the first thing where it crosses the x-axis. Different. Where we found that we're across the x-axis. And because we knew this thing a parabola quadratic function we knew it was symmetrical. So all we did, we took the average of negative 2 and negative 3 and plugged it into the equation, found the y and we found a place where it switches. It changes. Right? So we found this point here. It changes direction and goes the other way. Wow, cool. So what are some of the other important points on this graph? Well, where it changes direction is an important point. Right? Those are important points. There is another type of location on these functions, which are important. And those are where they change their convexity, I guess. In I didn't read the name what it's called. Masque of Raven will God, my differential equation is not to ask a raven. What's it called? Incidence? No, we changed the convexity. So for example, take a look at this thing. This thing going like this, so it's facing down, facing down, facing down. Over here, somewhere here. Okay. It was facing down and then it changes and starts facing up. Right? Inflation point. Thank you very much. Very much. Shin, nuk Shin. Okay. Inflation points. Yeah. I was just curious because I'm going to make these two classes part of my major. Awesome. This is an inflection point because the function here was like this and then over here it's like this. So where it touches is important. Over here it's doing the same thing. Inflation point. Inflation point. Right? So if you're able to make important points. The inflection point is where the convexity. Thank you very much. Dice power. I only looked at this thing for 15 minutes. I had downtime. I could look this up. It's where the convexity changes. So here and here and here. So once you realize that functions represent or an equation really that we've come up with to try to understand the world around us. Then what's important of a function is all the places where changes occur. Because if you can define the location of all these points you can graph this function and that means you understand this function. Right? The terminology is kind of goofy. Sometimes people use convex concave. Sometimes concave up concave. Yeah. I thought it was called concavity. I'm huge at the moment. It's about 20 minutes. What? What's going on? So take a look at this. This pen is, because I'm trying to write over this thing is there. That's coming up darker. I'm looking at the screen. It's not coming up as dark as I would like it. There is a point. So, how do we find these points? How do we find these crucial critical points? Well, we can use calculus. One way we can use calculus is we can look at a function and try to find out what the slope of a function is. Because when you find the slope of a function at a given point it'll tell you what the function is doing. Now, take a look at this. Here is a concavity. Let's take a look at this green. Oh, look at that green. That's nice. Dark. Hopefully it comes off easy. Well, not bad. We use this green. Take a look at this. Let's assume go back to this function. You're standing on here. How do we draw a sideways person? Let's assume you're standing here. That's a dude. Or a do that. Let's assume this person is standing here and they're moving along this function, along this line. At every point along this line this thing has a tangent. That means, just imagine what a tangent is. Just imagine if you had a ball, right? Attached to a rope and you were going around given momentum and this ball was going around this pivot and you cut it, right? If you cut it, the ball is just going to fly off in a straight line. So just imagine here is a point. Here is a ball going around this point attached to this thing, right? It's going around in a circle, right? And it's going at a rapid or not rapid pace. If you cut the string here, this ball is going to go right? It's going to go straight out, right? It's no longer constrained with the rope to go around this way. It's not going to take that turn but it's going to go straight that way, right? Now, that's exactly what a tangent line is here. From this point there would be a tangent going and it touches the function only at one location, okay? What calculus allows you to do is to figure out what the slope is at every point along the function, okay? How does that help us to find these points here? Because if we find those points there, we can graph this function. We don't need random points because these are the critical points. For example for this function for us to be able to understand it, this point is not as important as that point. Because this point here is continuing along the way it's doing. It's not changing, right? At this point all of a sudden it starts going down again, right? Those are the crucial points, right? Just imagine if you're driving on a road you can just stay on that road in a straight line and just keep on going. The only time that really matters that requires your attention, if there's a turn coming, right? If there's a turn coming then you have to turn with it, right? Over here the turn we're going to assume it's a straight line going like this until it starts going down, right? To a certain degree. It's not a straight line but you get the sort of analogy I hope, okay? So our main concern is how do we find these points? Right? Well, one of the ways we can find these points is these guys are easy to find. That's one reason they you learn about this. You learn about this in grade 10, right? For this guy all you have to do to find out where the function crosses the X axis is to set Y is equal to zero, which is exactly what we did here, right? We set Y is equal to zero. We set Y is equal to zero and we found these two points, right? So that part doesn't involve calculus. Given any type of function just set Y is equal to zero and find those points. Easy-peasy. The next important not straight but equally equally exponential. Yeah, this isn't straight but equally exponential. There's a rate of decline or rate of increase which is consistent, right? So if you're on a constant curve going like this, you can just put a little thing on it and just turn the wheel in a certain way and it'll just constantly turn in that direction, right? So where was that? Oh, yeah. You set the Y is equal to zero, you find your X intercepts. So congratulations. You found this, you found this, you found this. You learn how to do that in grade 10 and grade 11. The other crucial point you need to find is this, this and this and that, right? Where it's turning, right? It's either instead of increasing it's now decreasing or instead of decreasing it's now increasing, right? Well, think about this. If you're standing here, right? A tangent line here goes like this, right? So a tangent is a line and a line has a slope, right? To avoid your curve going like this, right? So a tangent is a line and a line has a slope, right? So this guy here, we'll draw it here. So from here the slope of this line is this, right? Okay. Now you can move closer to this point and again this thing has a slope. But what's going on and over here you have another point oops, that was a crappy line. So just imagine you standing here, right? Going on this curve and you're walking, right? So initially this is a steep slope and this one is getting a little less steep. This one is getting a little less steep, right? Because this is an equation of a line, right? So steep, not so steep less steep. At the peak here, at this point here the line looks like this. Now ask yourself what's the slope of this line? If you're walking on a flat road what's the slope of a road that's flat and horizontal? What's the slope of a flat line? Zero, right? So just imagine if we had a way to calculate the slope of this function at every point then all we would have to do is calculate find out where the slope of the function at every point on this line a slope of the tangent at every point on this line was zero. So for example here you would have the same thing this would go like this the slope there is zero. Here too the slope is zero here too the slope is zero, right? Wow, cool. So we need to have to come up with a mechanism to be able to some kind of technique to be able to find the tangent for this function, right? Find the tangent of these at these points on this function and that kicks you into calculus So for example watch this I'm glad we started with that actually this sort of relates to the quadratics For polynomial functions there is a rule you learn for when you're doing calculus there's going to be a whole bunch of rules I've watched these videos for years but this is the first time I'm turning it live I love your content but thank you very much for coming in live all ball, no shaft okay thanks for popping in live I shouldn't have read out that word the name is loud I'm just getting too tired of playing the pain is laughing so take a look at this thing let's assume let's assume we want to find where this guy the slope of this is zero right? because if we go along this guy and then let's do one more closer and then over here it's zero right? so what we need to do is come up with an expression at least the name isn't I'm not going to read that just imagine if you could find do something to this function to find out where the slope is zero well there is this is the way you would do it for polynomial functions it's ridiculously easy to take the derivative of the function and the derivative of the function is basically you're finding another function which gives you the slope of that function everywhere along the function let me say that again we can take the derivative of this function and the new function that we come up with is allows us to find the slope of this function everywhere along the point so the way you take the derivative of a polynomial function let me write it here plus six for polynomial functions it's easy all you do I'm going to write a generic one here that's assume a x to the power of n and then plus something else whatever it is for polynomial functions when n is apologies Yiccio disregard my handle I'm going to call you Shaft I'm going to call you all, hey all, how you doing so if you have y is equal to a x to the power of n plus the rest of it b x to the power of n minus one it's a polynomial function then taking the derivative is easy all you do you take this number here the power, kick it down and subtract the power by one degree ok so for example here you would go a times n and it would be x n minus one plus this term would be b times n minus one x to the power of n minus two now this looks way more complicated than it is so I'm just going to do it on here so you see how it looks for a polynomial function it looks like this you're going to take the two, kick it down x and decrease that by one degree so two minus one is one plus, what's the power on the one on the x this power is one so you're going to kick the one down so it's going to be five times one x and then one minus one is zero to the power of zero and the derivative of any constant is zero so six just becomes zero ok so plus zero so this becomes two x this becomes plus five times one is one and x to the power of zero is one ok so that just becomes one so this guy becomes plus five ok so the derivative of this which is you do this, you put a little thing on top of this that's not a power, y to the power it's, what do you call it y something ok so this guy here check this out, this guy here ok is the function of this guy but is giving you the slope at every point along this function right so it's one layer deeper one layer deeper of bit of information for this function so what we want to find out right now is and this is called the slope the derivative of y is this so if we want to find the derivative of y is this and we can graph this guy by the way here, watch this x this is y prime right so five one two three four five and then up to over one that's what it looks like right so that line is the function that gives us the slope of every point along this parabola right so we want to find out when is it zero when is it zero, ok just set y prime the derivative of y to zero, y prime, thank you very much Catholic tradition I forgot all my terminology right so what we're going to do is we're going to set y prime to zero let's set that to zero is equal to two x plus five grab that guy bring it over negative five is equal to two x divide by two you get x is equal to negative 2.5 what but we knew that take a look at this thing this was negative two this was negative three this is a parabola and the middle was negative 2.5 we're at the vertex we're at the point where this thing switches up right changes holy Kamolis right so what that means is if we want to find what the y value is there just take x is equal to negative 2.5 plug it back into the original function and find your y and we already did that before we started this example and this becomes negative 2.5 and negative 0.25 you just found the vertex of the parabola guess what you can do this for this function if this function let's say x to the power of one two three four five should we do it for that one can you see this far down you can see this far down I'm going to write something down first this let's assume the graph of this function is the following or the equation for this function is the following y is equal to one two three four five two x to the power of five plus three x cubed plus two x squared plus one now I didn't include the x to the power of four I didn't include x to the power of or just x to the power of one so let's assume this is the equation of this function and we want to find this point that point so what we're going to do is take the derivative of this function because the derivative of this function is the equation you need to find the slope at every point on this function and what is that going to allow us to do well we want to find out when the slope is equal to zero so we're going to take the derivative of this function equal to zero and to find the x's associated with that zero point right so what we do is take the derivative of this this is a polynomial function so you take the five bring it down it multiplies the two becomes ten and you kick this down one level right so it's x to the power of five becomes x to the power of four plus you take the three bring it down multiplies the three becomes nine x and x to the power of three you kick it down one level it becomes x squared plus kick the two down this becomes four x and a constant becomes zero so the derivative of this function well this is y prime now right y prime the derivative of this function is this guy that's the equation for it right so if we want to find these points all we do we set y prime equal to zero okay so zero is equal to ten x to the power of four plus nine x squared plus four x okay is that cool it's the rate of change exactly chicho I've just realized I'm not ready to help my nieces when they get to high school Martin you will be you have a mathematical mind they're learning learn with them really you the mathematics you're going to learn you're going to go what you first thing that's going to happen to you when you start learning math to help your nieces right because this by the way the reason I started creating videos online okay really I first videos I loaded up were on Vimeo daily motion and YouTube in 2007 I started making videos because I was helping my nephew I was in Vancouver he was in LA right and he was having a hard time with mathematics and the way I knew to help him you know just doing it through email and phone wasn't working so I started making videos to help him okay so check this out right now if you're into calculus then you should be able to find the exact x points where this is equal to zero you find the solution to this right so once you find the x values what you're going to find out is you found this point you would find this point you'd find this point and you find this point right whatever those points are we're not going to do it right now but whatever those points are you need to do synthetic division to this to a certain degree you can factor out an x you factor out an x one of them is x is equal to zero we pick one that worked right so this is x is equal to zero you factor this can we go down one level watch this zero is equal to x you can factor out an x from here so this is 10x cubed plus 9x plus 4 right the power of zero is you got things multiplied to give you zero so x can equal zero and this can equal zero and then you factor that that's x cubed you need synthetic division to do it okay there's 3 and 2 at the moment that's funny I don't think okay so once you do that you'll find this point this x value let's call this x1, x2, x3 we already found this one which is x is equal to zero then what you do is plug these x values into your original function and you find the y associated with it so congratulations you just found the inflection point where not the inflection point the maximum the relative maximum that changes and then you would find the relative minimum and then you would find the relative maximum and then relative minimum and keep on going keep on going that's what you're doing when you're doing calculus okay now the way this works is the way we're taking the derivative here is there's a fundamental theorem of calculus which is I was actually going to teach that instead of going into this but for some reason I went into this because this is more of the application the understanding of it because you don't have to do the fundamental theorem of calculus every time but let's assume you just want a little taste of it the fundamental theorem calculus says this f prime f of x and we have to use f of x when you're getting into calculus you're using f of x right? f prime of x is equal to the limit limit of h approaching 0 of f x 0 plus h minus f x over h okay and what this is is really how you take the derivative of a function okay now for polynomials it's easy you do exactly what we just talked about you take the power, bring it down, multiply it but whatever coefficient was in the front and reduce the power of the polynomial down one for other types of functions it becomes more complicated now how's our time? should we do one using the fundamental theorem of calculus? I don't think so we could do it, business calculus but I would have to explain the process the process is basically you would do this if you have a function I would have to erase all this stuff you go from one point to another point you draw a line segment and you get closer and closer and closer where h approaches 0 and you're simplifying your functions until you're able to get an expression for it but I think I'll stop the calculus part there sort of an introduction to calculus I hope that was made sense for anyone that's interested in watching this live right now and anybody that's watching this after the fact right? when we load it onto BitShoot and YouTube but that's basically what we're doing and the inflection points here the inflection points here you find by taking the second derivative of the function right? so you take another derivative set it equal to 0 and you find your inflection point I believe anyway or you find the place where it goes from is this positive, negative pointing down and positive pointing up I think that's what happens Catholic traditionalist I remember my first day of calculus class in college the professor showed a derivative of the fundamental theorem of calculus he told us that we would not understand it but that he expected us to enjoy his presentation like we would find symphony nice and we can do it should we do what? it's brilliant that's right it's super fun, is that right? a thumb? that the negative is down and positive is up, right? I think so because you take the second derivative set it equal to 0 and you find where it's going from negative to positive and congratulations you found these X values here right? and then you plug them into your original function and get the Y associated with it so congratulations you found this point and this point and this point yeah super cool stuff like really by the way the first time I took calculus I didn't understand it really I didn't understand it I failed the first time I took calculus again at a different university I wasn't really into it and this is the book I read to teach myself calculus because I learned nothing in class unfortunately yeah you find the critical points where the slope is 0 awesome, right? fantastic and this guy here we can do an example here I'm going to erase all this let me erase all this here let's find the derivative function using the fundamental theorem of calculus I failed two times and I understand it I feel you like for me by the way I remember the moment the moment where calculus went woop brilliant, right? I was I was in the library two months into a four month term course for calculus okay and I was just what did I see monkey do? I just wanted to pass the course I was reading, I was reading I was doing examples, I was re-know and then also when I click I went what? and then I went back to the beginning of the book and reread everything that I had done before and it was so simple, so easy it made complete sense and the reason I remember it because I was sitting at the library I was by window listening to classical music blasting it on a CD-ROM player so I learned calculus listening to classical music and I highly recommend it I think I was listening to Bach some piano concerto symphony, something the daily industry as well the secret is yeah, same I was hitting a wall for months then it finally started making sense and I was like, it's simple once it clicks, it's so simple once it clicks I listened to Bach you listen to Bach too, Bach is the answer when you're studying calculus listen to Bach to learn calculus really let's use this to find the derivative of a function okay let's say we have a simple function y is equal to 2x plus, what was it, the number we had 1 let's say we want to find the derivative of this function okay, should we do it more complicated should we do quadratic no, let's do this okay so what this thing says is this take the function and introduce an h into it so y' which is f of x' is equal to limit as h approaches 0 of x0 plus h, so wherever you see x you're going to sub this in so you're going to go 2x plus h plus 1 minus 2x plus 1 all divided by h okay please keep it simple so take a look at this that's 2x plus 1 but what I did I just said x plus h it's like saying find y when x is 5 find y when x is 5 you just plug 5 in for x and you solve it over here we're saying x plus h so we plug in x plus h okay thank you listening to barok burak like that of and valdi has been shown to improve focus, does it burak, how do you pronounce that barok music where is that from catholic traditionals like highly recommend classical music or as catholic traditionals says barok baroky music okay so we're going to expand this so this is the limit as h approaches 0 of 2x plus 2h plus 1 minus 2x plus 1 all over h and then you simplify I listened to Wagner music of national socialist alcohol lords does not oh we got a troll coming in what's this let me kill the troll before you extend I'm not going to ban you yet I'll let the moths take care of you okay so we're just going to simplify this right now watch this limit as h approaches 0 so 2x minus 2x they kill each other 1 minus 1 they kill each other so we got limit as h approaches 0 of 2h over h well that's limit as h approaches 0 h kills h 2 limit of 2 h approaches 0 is 2 so the derivative of this y prime is 2 well is that true that was 1, our rule was take this multiply it by this 2 times 1 is 2 and this becomes x to the power of 0 is just 1 and that's 0 hey that's correct we just use the fundamental theorem of calculus to figure out the derivative let's do a more complicated one the quadratic music is a period or style of western art music composed from approximately 1600 to 1750 explains how to make a derivative the long way let's make it a little bit more complicated let's use a quadratic but a simplified quadratic let's say we have 2x squared plus 5 okay so what we're gonna do is we're gonna use that guy so we're gonna go plug in x let's just call this x plus h we're not gonna call it x 0 so wherever you see x put in x plus h so 2 x plus h squared plus 5 minus because we have a minus I'm gonna put this thing in brackets 2x squared plus 5 all over h okay thanks for simplifying it for me and not betting me very bored during this time don't be bored and be nice we have an amazing community here it's all about empowering just giving people the tool that they need to relax, chill, enjoy, cook, eat exercise and learn mathematics which is ridiculously powerful okay we're doing math to fight off the boundaries really the Catholic tradition is I like limit as h approaches 0 of 2 we're gonna foil this out so you guys see what it is so x plus h squared so x plus h times x plus h so you get x squared h plus xh which is 2xh plus h squared right so this becomes x squared plus 2xh plus h squared plus 5 minus 2x squared minus 5 all divided by h okay multiply the 2n limit as h approaches 0 2x squared plus 4xh plus h squared plus 5 minus 2x squared minus 5 all over h right now we simplify 2x squared kills 2x squared positive 5 kills negative 5 we're stuck with this right so now we got limit as h approaches 0 of 4xh plus h squared all over h okay now factor out an h so this is limit as h approaches 0 of h 4x plus h over h h kills h so this equals the limit as h approaches 0 of 4x plus h right well as h approaches 0 h just becomes 0 so the derivative of this is just going to be 4x so y prime is 4x is that true let's check it out according to our simplified version is you take the 2 bring it down right 1 prime is equal to 4 and this becomes you kick this power down 1 so it becomes x to the power of 1 derivative of a constant is 0 so it's 4x 4x awesome awesome okay and that is calculus we got the visual of what it is we're actually trying to calculate which was finding we're coming up with an equation that gives us a slope point for the original function right wow cool hey when is this thing equal to 0 when do we have an inflection point when h y prime is 0 right I turned 47 to September assuming it's not resident evil world yeah I like the shortcut I like the shortcut as well you don't have to do this you just have to learn the shortcut right and all the different types of functions have shortcuts with them fun this is the first time we're doing a full blown calculus math thing it all it took was a little bit of incentive from someone requesting us to do calculus for me to look at this thing speedy bonzala style today just to refresh it to do this I hope that was clear of what it is that we're doing it gets more complicated with word problems and integrals yeah integrals is the reverse of taking the derivative of it in the other direction you're finding the original function if you want to think about it right that was a good explanation okay thanks I don't think I skipped over anything important I think it it should give people a pretty good idea of what calculus is and what to do with it okay and it's good I've had a lot of people ask me for calculus so it's about time we did one you're setting up precedent you might have to do some more calculus I know I know Catholic traditionalist I've been waiting for the summer to come along where I have more free time to start reading this again and relearning it to be able to teach it again right it's just right now I don't have the time that's required to put in to teach it properly right but I think we did a pretty good job thanks to you guys by the way for giving me the terms and the terminology in correcting me right but I think we will have to at some point it's important I've had a lot of people ask me for it like crazy number right but right now I've sort of gone in the other direction here's zoom play 3am you're in UK I've gone in the other direction right now I have a lot of students that are in the early stages of learning mathematics and I'm really enjoying teaching that starting with addition and counting and taking them all the way into division and dealing with fractions and solving equations it's really fun really fun after all this math I need a beer but it's 2am 2am here Martin you own the place you can hit that thing anytime you want but don't do it I have time to spare oh brother I'm actually craving right now too I don't want to hit it I learned calculus in the summer course 4 weeks for 4 days for 4 hours a day best way to learn it, dive right in always be making I agree with you dive right in you just have to make sure you have the time required to really let your mind just flow with it because with calculus you really have to just let it sink in and just go wow watch it in awe right and learn it in awe dice power I had an integral question if anyone knows the answer what is the indefinite integral of f of x f of x y of x dx that is the integrand is a function of x and another function of x beyond me dice power someone might be able to have dice power in discord there are people offering their help for mathematics so you could post it in our math folder it's on the heavy topics should be maybe in the light down heavy topics for sure we have a discord page so if you post it in that folder maybe someone will be kind enough to help you out yeah used to study 3-4 hours a day to be able to get used to it yeah me too me too you have to many things worthwhile learning require the energy to be put in to learn it hello boss man xerox I have just stumbled upon the stream and I would like to thank you for providing free tutoring even though I haven't thought about math for years bless you jesus thanks for popping in sure and this is by the way I know people appreciate this or find it but it's also for self-preservation for selfish reasons because it is my belief if the whole world was literate in the language of mathematics we would be in a much better situation than we are right now all of us would be right so I do this to improve my life because I think if society all literate in the language of mathematics everybody's life would improve you wouldn't have shenanigans by corporations and politicians and special interest groups pulling the wool over our eyes curtain over our eyes and fooling society into supporting their genocidal like insanity right when you learn mathematics you can see BS coming a mile away a mile away you can just say BS BS BS that's good, come on that's true there have been people put in jail because the juries had no understanding of conditional independence it's insane try to convince people that logic is greatly missing in society and the reason for that is because most people, many people are illiterate in the language of mathematics is very difficult true boss man I can tell you why it's the goatee and eating homemade cookies with homemade applesauce and mandarins eat well there there are whole wheat check this out whole wheat okay whole wheat coconut flour honey, chocolate chip cookies with walnuts that I made like four days ago with homemade applesauce that I made like a month ago and an organic mandarins very good by the way I've got to try that I have the recipe online we've done two live streams where we made these honey, chocolate chip cookies okay if you do chicho, honey, chocolate chip cookies or cookies there should be two videos where I show how to make this this is sort of a modified version I put coconut flour in it and stuff but it's the same recipe chicho I'm downstairs I have a pint glass of my own I'm looking at the side of her pommel are you solo martin? are you solo? is it on your youtube? yeah, it's on my youtube chicho chocolate chip cookies let me see if I can find that speedy ones Alice for you let me see if I can find that speedy ones Alice chicho cookies chicho cookies maples this is the original one we made one that was a live stream as well this one is not the live stream but there's another one that's a live stream as well here's the original one we made and there's a little intro for it too I'll give you the intro, the intro is like 8 minutes it gives you the recipe you can see the setup let me make sure it doesn't start chicho cookies man like martin oh you found it awesome and there's that one and then that links up to the original one and then we did another one I think we've done a live stream of it I guess it would be considered calc one yeah, introduction to calculus by the way it's interesting to see that the math where you are and the math where I am in France are the same math is the same everywhere international, right? that's the beauty of it we can communicate to everyone around the world irrelevant of their natural language through mathematics it's brilliant may I post a poll for a class about automated vehicles it's four short questions you know what, we're about to end the stream brother or sister of course and post a question there and you're welcome to pop in and post a question in future math streams that we do oh martin you already hit it up okay cool thanks, that's awesome there's a certain university to the language yeah, universality to the language of mathematics that's one nice thing about math don't have to relearn math in another language don't mathematics is as beautiful as a language as Italian or French so we're almost at the end of the stream where we are at the end of the stream just to let you know, this is our Patreon page okay, if you want to support this project Patreon is an amazing way to support this project and you don't have to support to follow you can just follow and you'll get updates of what we're posting and stuff like this and I do post all the videos there stream sets there and share some other information there as well okay, we are live streaming this on Twitch so if you want to watch these things live I know you guys watching on Twitch right now live, you're going, why is he saying that because we want to upload this to BitShoot and YouTube and other platforms possibly in the future okay, but we're only live streaming on Twitch right now I'm subscribing with Twitch Prime or Tier 1 and stuff is also a great way to support this project if you have the means to do it oh, YouTube as well thank you for the love people thank you for the love I announce these things on Twitter, Gap, Mines, VK and Elo, right those are the sort of announcement platforms that I'm on okay, so you can follow the work there we do upload these videos to YouTube in BitShoot everything on BitShoot, almost everything to YouTube right now everything to YouTube because we're in a pandemic so the sensors, maybe they're in hardcore more maybe they're not we're finding our way through the cracks okay, and we just recently got approved for YouTube membership so YouTube membership is again a nice way to support this project as well okay, 4.30 am UK time I will be there let's talk greed oh, the economics one, that's right that's right, okay and we are during interesting times during the pandemic lockdown and flatten the curve is a good thing to do make sure you don't stress out your healthcare systems wherever you are because this line that you see there is the capacity of your healthcare system to be able to take on patients you want to make sure you're below the line because once you go above the line if hospitals, your healthcare providers are overwhelmed, what's going to happen is everybody's not going to get good care, so there's going to be people sacrificed and healthcare workers right now, and the cleaning people right now, and all the people who are considered to be critical work people that are working right now, are putting their lives on the line to protect everyone else make sure you respect that work okay, don't put them at risk just listen to the general consensus right now that it's the best thing to do to keep a little bit of physical distance it's not social distance, because what we're doing here is social very social it's just a little bit of physical distance there's a storm outside, bunker down chill, until the storm passes and then you can do everything else you want to do okay, thanks for being here thank you for the support thank you for the feedback thank you for the conversations mods, thank you for taking care of business good evening everyone, thank you catholic traditionalist thank you everyone really, okay, chichonians is rust your land is in land is it russ? russ okay, and tomorrow we're doing economics I believe and then we're doing education and then we're doing next three days we've got streams lined up 8.30 p.m. and 8.30 p.m. next couple of days spider-man, awesome awesome I think we're doing economics, personal finance investing tomorrow I think we're doing education the next day, today is Wednesday, so Friday and on Saturday we're doing mental health in the afternoon I believe or in the morning I think from 10 to 12 or something in my time okay take care everyone I hope you have a fantastic evening and I'll see you guys tomorrow awesome, peace everyone