Concavity, Inflection Points and Second Derivatives

[halhauder79]

can you help me solve for convexity of the function y=e^-x^2

thanks

[lookitsbrandon]

Thanks for the help! You got me through my last unit exam and hopefully the next! 

[iloveBeaver1]

my calc teacher won teacher of the year a couple years ago, but can I just say, while hes a fantastic teacher, your videos are whats getting me through math

[patrickJMT]

@iloveBeaver1 glad you like my stuff : )

[wolf0805]

Scary noises in the background.

[MrLexisyomasta]

thank you

[japanesefool01]

patrick, will you adopt me? Lol...or will you let me have you brain?

Gah Calculus is so stressful. Ive fallen behind in two major topics in my calculus class. And im kinda lost.....(RELATED RATES and OPTIMIZATION)

[korcagin1000]

you are the best man thx

[cuyes1223]

WHATS UP WITH THE STICK FIGURES AT THE BEGINNING?? LOL

[ghostMI305]

are you kidding me??? you spent half the time doing Bullshit factoring and skipped the most important part at the end?

[KayaGold]

You're like my calc teacher.. but I can stop and rewind you

[brittlette14]

Can you tell u whether to include the points or not? like bracets or parentheses

[IBLiiitZz7]

Patrick??? will you marry me? so you can do my math work for me. just a heads up I 100% MAN

[patrickJMT]

@IBLiiitZz7 pdiddy don't swing that way

[susanhong99]

u can really make these problems sound so easy!! :)

[deathcommand]

Off to my math final. Hope I do well!

Thank you as well!

[lomgandsomejelCO]

if i do well at all on my calc final, it will be one hundred percent be because of your videos. thanks!

[patrickJMT]

@lomgandsomejelCO good luck : )

[zkartje]

The videos are great thanks! But I was wondering to find inflection points...

I know wherever the concavity changes is the point, and the x value is the value you use to test the concavity, is the y value found from plugging in the x value into the second derivative?

[chinshihuandi]

@zkartje do exactly what he did to find the zero points on f''(x) and the concavity by using values between zero points and interpret the data. inflection points are where concavity changes. so by looking at the data you can see where the concavity goes from + to -, or concave up to concave down. look at his data, at -1 on the left side its positive on the right side its negative. therefore it is an inflection point. cocavity changed. caution, not all zero points are inflection points

[zkartje]

@chinshihuandi Great thanks!

[chinshihuandi]

@zkartje no probz man, got anymore questions i wont pretend to be as smart as pat but im a college student with alot of extra time so feel free to ask anymore

[buccos2324]

Great idea to do all the work in markers! I notice that my math gets better when I'm doing that. This is great stuff. I hope you get filthy rich off this and that Youtube pays you well!

[konichiwasupersan]

These videos are the only way I am passing Calculus! Thnx so much!

[cutediva784]

ahhhhhh thank you so much. you just made my life so much easier lol :))

[ghidfg]

nice thx for this

[biboo296]

i love this guy 

[lilythatgirl]

I just wanted to thank you so very much for the amazingly easy to understand videos which you have posted all throughout Youtube. I got a 97 in calc b/c of you PatrickJMT!! Keep it up! :)

[patrickJMT]

@lilythatgirl congrats on the good grade : )

[maxolive94]

@patrickJMT fraction on the *bottom* of the equation

[maxolive94]

@patrickJMT so if you have a fraction in the equation would you also set that equal to zero in order to find a point of indifferentiability?

[serpentphoenix]

why do commercials pop in during the middle of the video?? >:/

[patrickJMT]

@serpentphoenix thanks for letting me know. they are gone now!

[flarexdragon]

u saved my ass man, u rock

[ilovgoogle]

When I become rich and famous I'll shower you with money to run a math empire that extends across the globe. You just wait and see....

[patrickJMT]

@ilovgoogle ha, ok, i will wait : )

[snoopylover8]

Dear Patrick,

Thank you so much for uploading all of these videos! I know this is bad, but I occasionally I fall asleep in my AP Calculus AB class and miss parts of the lesson. Your videos are PERFECT for filling in my mental holes. I really think Youtube should give you an award or something for your contributions. :)

PS i love your handwriting.

[OhhCaptainMyCaptain]

@snoopylover8 do you go to rio? not to be creepy or anything.. but if that name means nothing to you.. please disregard this comment

[OhhCaptainMyCaptain]

@snoopylover8 nevermind.. unless your a month in the future

[snoopylover8]

@OhhCaptainMyCaptain haha No, I do not! In fact, I've never even heard of such a school. I'm assuming u know a person who falls asleep in class a lot? haha

[DominoChild]

Where did the 4x^2 come from?

[JustDoWhatITellYou]

would both -1/rad5 and +1/rad5 be the points of inflection? 

[astaple10]

Thank you sooo much!!

[patrickjohn84]

This video >>> Stewart Calc 6e. Thanks!

[Kapurod]

Ah, just take -0.5 as the last value between -1/sqr5 and -1 :)

[loveiszen]

You should be sponsored by Sharpie. 

[holypupppet]

Because what you found are the inflection point, after you graphed them, and found the concave up in the numbers bigger then one, you already know that before 1 it's concave down, and before that concave up, and so on, you didn't have to found each point separately. 

[scorpionboy3]

I appreciate your work in making this videos, but i miss the why in the things you do, i mean your videos help in solving exercises, but sometimes are lacking in what´s going on and why are we doing what we are doing, and that is what´s interesting, not passing some test. If you would talk a little more about the why in your videos, it would be the perfect resource for learning. Thank you for what you´ve done so far anyway!

[bevon17]

yeay i is smart now =)

[rami62392]

ok i really need you to work out a fraction

[mrhozer]

I'm pretty sure if there is a shift in concavity, and all surrounding points are concave up, the interval between should be concave down

[B15h73k]

thank very much. BTW you have nice handwriting, much easier to read than my lecturer :)

[noseasmamut]

Patrick thank you so much for your contributions to the world. You have decreased the number of headaches caused by calculus. Again thank you.

[kgmahabir]

god bless

[garhettcarrot]

Patrick, you saved my college career. I was coasting in business school until I had to take math again. I was lost, then found your video collection and was saved! Yours are the best on youtube, PERIOD. You have my gratitude. You are a gentleman and a scholar.

[patrickJMT]

@garhettcarrot thanks : )

[vintagIee]

You're amazing.

[camarosam]

Thank you!!! The TAN; Applied Calc book sucks, they show no examples of any problems. And my teacher isn't really into it so that isn't helping either.

[H3llfire741]

i love you patrick

[obese1pandas]

my gosh 1000000000x better than my calc 12 teacher's explanation

[ThisIsMe812]

ugh, i have a question. i'm really having a hard time. what if the function is like this: 1296x - 0.12x^2 ?? how am i supposed to know its concavity when there's no x in the 2nd derivative?

[adamska4]

@ThisIsMe812 If there is no x in the 2nd dy/dx, then the concavity is simply determined if the number is positive or negative. If positive = concave up, if negative = concave down.

ex.) Find concavity of x^2

(1) dy/dx'' = 2 ... Therefore, concavity is always up for all values of x.

Hope this helps...

Source: Gr.12 AP calculus

[Knifeinyourback]

I really like your videos but what theorem or rule just let's you ignore the + sign near the end when you're looking for zeros and sub in brackets?

[TheAlbania91]

I love your voice!

[patrickJMT]

@TheAlbania91 i sometimes turn on about 20 different random videos of mine at the same time and listen to them

[bossbower]

@patrickJMT haha

[TheAlbania91]

@patrickJMT

lol , weeell... I'm still grateful to you :)

[sonicr007]

"and ill..." ILL NEVER KNOW!!!!!!!

[EcFXSN1P3RX]

sir... you have successfully save my life...

[KrisSavvys]

all your vids are helping me alot for my upcoming tests and my midterm next week haha. very much appreciated man

[crazyweathergirl]

damn. he's got on a wedding ring. :/

[Kingboy676]

thanks man u make me love math THANK YOU

[MrHav1k]

Keep this up and there will be a lot of jobless Math teachers....

you're AWESOME!

[KoreaXFan]

HI, do you have any lessons on Inflection Points?

[lloja443]

fuck commercials ...for real though

a waste of time

[patrickJMT]

@lloja443 you tell those commercials, tough guy!

[djrook727]

Thanks for the video! AWESOME!

[skrevat]

Just wanted to say-- My math department steals problems from MIT, and this is the exact first example they had me doing in my homework. No coincidence- you're a great teacher!

[sjdrury]

i spent all of this week doing nothing in class, and watched then i this one video.  thanks for making laziness work out for me!!!

[nicgatornic]

just to let you know, your 10 minute video helped me more than my teacher teaching me this for 87 minutes ahah thank you for these videos

[RuthBuzzzzz]

thx! now I'm pretty confident about my calc test tomorrow! :)

[MustangRacer13]

You are honestly a life saver! You explain things so thoroughly :) Thank you for being nice enough to do this on your free time for us young math students.

[gelucadri]

It help a lot!! tx! uwo

[zoom2121]

Do you have any videos which show how to find inflections points?

BTW your videos seriously helped me a lot in CALC 1

[patischadillac]

@zoom2121 The inflection point in the first example is 1; you find the inflection points by making the 2nd Derivative = 0.

[Soviless99]

got a quiz on this shit tomorrow, my algebra is weak and skipping steps of simple stuff gets me lost even thought i know what to do if i work it out

[Edddddyz]

Ever thought of working for Evergreen Valley High School

[patrickJMT]

@Edddddyz no

[middlecollege]

One word:ILOVEYOU!

[patrickJMT]

@middlecollege lol, that is one word : )

[THEAEGHOST]

i would make love to you if given the chance ^_^ lololol, please come find me, we'll have a good time...i promise

[Mikavos93]

Thanks a lot. Your vides help so much !!! :)

[tso5678]

I hear a car horn in the back did you get carjacked

[manshet1]

@tso5678 you know what, it made me cray during the video.

[tonewaf]

hey patrick i have a question if im trying to find concavity can i take first derivative of the function after that, set my first derivative to zero and find my critical points. After thats done get the second derivative of the function then take the critical points i got from the first derivative and plug them into my second derivative depending what my answer will be if it is a negative its concaved down if its positive its concaved up.

[ShallowBeliever37]

you have beautiful handwriting ^-^

and your lectures are very useful. thank you ^-^

[ScotleCyphez]

an easier way to find the two parts at the end is to plug in numbers such as +/- route 1/4.

it works nice because its a route function being squared, so youll get easy to work with values.

[gyhighway]

This is great stuff, Thanks alot!!

[finestbravest]

Patrick you are by far the best instructor... Thank you for taking the time to do this service. MUAH!!!

[JIAQIR]

i find it is really hard to keep my Math mark over 95..but now,,at least 50% of getting a 95% is here..'

[blitzforce]

@JIAQIR ur tests must be insanely easy if u could get 95% with this knowledge

[JIAQIR]

@blitzforce i said that just because i wanted to tell patrick that he is the best teacher ever. plz be nice. ok? well.. i can say.. i am better than you no matter what.

[patrickJMT]

@JIAQIR hahah please, everyone : )

thanks for the compliment

[JIAQIR]

thats soo helpfull... i was crying for knowing nothing... but now...i know everythin is gonna be fine..

[Jay0929]

Thank you!!!

[AlaaJassar]

THAT IS AWESOME

[asjanjua]

dude this is excellent. I am doing calculus after seven years and now using it in my masters and your videos especially this one helped me alot. <thanks

[miv3c]

If it wasn't for your videos, I wouldn't have passed precal 1 & 2 and calc 1. Thank you so much!!!11

[sistagirl63]

very helpful!!

[rapture2100]

thank-you!!!!!!!!!!!

this is fuuckin awesome.

sorry for cursing, but you saved me

[dual85]

Okay. So why use second derivative test when the first derivative test tells you whether its concave up or down.

[xixxon]

the first derivative test doesnt tell you whether it's concave up or down, it only tells you if it's increase or decrease. A graph can be increasing while concave up in the first interval and concave down in the second interval at the same time. maybe your book will have some example of that

[333329753]

@DJPirrone

you are great human being ... but you gota stop commenting like a fag...

i tried my best not to swear... :D

[domain300]

Maybe YOU should stop ACTING like a fag and appreciate his videos.

[HeroOfXanadus]

@333329753 I don't fucking understand..... YOU. so stfu and go somewhere else if you don't like him commentating.

[staind2523]

My calculus book...is terrible at giving clear examples (Some are good but are either too easy or are exceptions to the normal problems)...so thank you very much for your examples. Makes the whole process a lot easier.

I can't imagine how many test scores you have single handedly improved solely because of these videos.

[waspy89]

I want to mention one clarifying point. You say "in the same way, we take the first derivative and set it equal to zero... we take 6-6x and set it to zero". Anybody really paying attention would realize 6-6x is the 2nd deriv but just based on the wording it's possible to think you get crit points by setting 1st to zero.

[zipmcoccup]

Yeah I got confused by that too, I had to think about my whole life for a couple of seconds.

[autumnofmyheart]

with your videos, I don't even have to hit the textbook. I LOVE YOU

[manson666korn]

Yes thank you for you videos. Also, I think the derivative is also very useful in finding a point of inflection to confirm that a change in concavity exists. Ohhhh and yeah i agree i havent taken any math in 4-5 years and going in to calculus made me lolol because the calculus concept part is easy but the algebra killed me because its been so long since i've practiced algebra 2 :(

[trunker420]

yep I've had the exact same experience. Luckily we have Patrick here to help us with our algebra too!

[emerson9223]

Thank you for your help and clarity!

[bravocone]

hey i have a question,

when you have the second derivative equal to zero, and x does not exist.. then what happens? =S

[Tehhunter1]

Just out of curiosity, are you an actual teacher or not? Because you do explain everything very clearly.

[BlueElectric13]

thank you so much! i learned a week of calculus within 30 minutes thanks to your videos!

[filipinoguy54]

i think it will be more helpful for ur viewers if u use a table containg the interval of those value of x in the second derivative...

[krazybones09]

i have 1 question

why does this look like this??

f"(x) =6(x-1)(x+1)(√5x - 1)(√5x - 1)

why does 5 have square root??

is it bec. of x= positive&negative 1/√5 ??

[Kh0nlao]

I've noticed in Calculus that the problem doesn't come from Calculus itself but the intense algebra you have to calculate. It's a pain...

[patrickJMT]

yep - algebra is the #1 reason that students fail calculus, in my opinion

[MetallicaFTW7]

wait... you set 6-6x=0.

thats the second derivative... you want the first derivative set equal to 0 dont you?

[patrickJMT]

first derivative is used to find increasing/decreasing local max/mins

second derivative can be used to find concavity and local max/mins (usually)

[idaho777]

@patrickJMT you said that the first derivative and the second derivative are used to find local max/mins. is there a difference in the X value when finding the max/mins in each derivative?

[danak281]

can you take my quizz tomorrow?? lol!

[patrickJMT]

probably

[ghst1203]

Thank you for your help! You speak very clearly and you teach it well.

[future08star]

maybe i wouldn't such at math so much if everyone taught it the way you do

[sleepingbeautyy6]

thank youuu

you are the best....wish i u were my teacher :-)

[motovidman]

patrickjmt is my hero. just thought i'd throw that out there.

wish i'd discovered these sooner than the day before my final exam! keep up these videos!!

[maycanadian]

its helpful

[Haroson]

I wish you were my teacher!

[jugedblue]

i was just about to write the same thing :)

[nishibd974]

@Haroson i wish it as welll....im killing my self now for dis calculas even in my holiday.....:(

[jchrisjj]

OMG Thank you!!! i am going to use your videos all the time now since sometimes i dont understand my Calculus Teacher........... THANK YOU!!!!

[xp80000]

i love your video so much..it's very helpful..

[HeyWheresKel]

man, your videos are so helpful....

i seriously need to refer to them more often.

[megazilch]

your awesome...

[patrickJMT]

yes! absolutely correct

[smckenna162]

Someone's car alarm is going off during the whole video lol.

Thanks for the help! I was having a lot of trouble with this concept

[patrickJMT]

yea, it sure was : ) c'est la vie

[matingwarhawk]

its people like patrickjmt who open my mind to the beauty of calculus

[patrickJMT]

aww nice! : )

[samurai165]

wow thank you very much, really helpful!!

[leapoldstotch]

college teachers teach you WHY the equations you use are equations! Where do they come from? How is that true in real life? Like with a real graph....

[patrickJMT]

i am not sure i understand your question... : )

i do not tell anyone why the equations you use are equations... they are equations cause they have an ' = ' sign in them!

[leapoldstotch]

Knowing how to do solve these problems is not the hard part guys!! its obviously easy as hell, EVERYONE. The hard part is understanding what it means, "the line is bending up so its concave up". That would be false on a test... the answer would be it is concave up because the second derivative is greater than zero. UNDERSTANDING WHAT IT MEANS AND HOW YOU USE IT IN A REAL JOBS IS WHAT MATTERS!

[RocknRollDina]

thank you.

[patrickJMT]

no problem!

[cjy2k6]

Dude you need something about "the first derivative test"

[patrickJMT]

i already have two videos about this stuff on my website! not all of my videos are hosted through YouTube so check my site as well.

[SeanieC21]

At about 2:10 you say to find where the 1st derivative is 0 or undefined, but then you use the 2nd. Does it matter which is used?

Thanks!!

[clout90265]

of course it matters. the 1st derivative is for inc/dec.

and the 2nd derivative is for concavity!

[DatCatTheyCallQueen]

Hey at about 6:30 you set the second derivative egual to zero but you left out the "6" in that step then you plugged it back in but i dont understand how the second part came out to "[square root of 5(x) - 1]times[square root of 5(x) - 1]" can you please explain

[patrickJMT]

once you have it factored, you set each part equal to zero. since 6 can not equal zero, we just leave it out.

and for the factoring part: i use the difference of perfect squares formula:

x^2 - y^2 = (x + y)(x - y)

so to factor x^2-1, use x^2 - 1= (x + 1)(x - 1)

and the same thing on the 5x^2-1 part!

[poisonIVY004KG]

when you collected like terms, what happened to the whole number 2?

[patrickJMT]

at what time in the video?

i could have made a mistake!

[adamfattah]

Thanks man, very much appreciated

[ekim88983500]

nice