Finding Critical Numbers - Example 1

[wolf0805]

What is an example of when it is undefined and in the domain?

[moonira0209]

What does he mean by domain? Wats the domain here?

[patrickJMT]

@moonira0209 the domain of the function... videos on that too : )

[vindrila]

I should make "Thank you" auto comment for your videos ;)

[patrickJMT]

@vindrila ha : )

[brittnibeers]

I DON'T UNDERSTAND WHY ISN'T 3 AND -3 ACCEPTED. Critical numbers are defined as f'(x)=undefined so why why WHYYY ;A;

[patrickJMT]

@brittnibeers you should read the definition a bit closer for critical numbers.

[iixsarah]

but arent critical numbers x-values such that f'(x)=0 and/or f'(x)=undefined? so why can't -3 and 3 work? if you plug it into the derivative, it's undefined..

[reedOsama]

@iixsarah the derivative f '(x) needs to be undefined but if you plug 3 and -3 into the original equation f(x) it's also undefined which means it doesn't exist on the graph... at least that's how I understand it.

[patrickJMT]

@iixsarah the values also have to be in the domain of the original function. this is the part no one remembers!

[fuzzylumpkins219805]

Holy rap i hit dislike by accident! o.0



[ASunDr]

Never mind, sorry, I realize it is because when you move the denominator over all you have left is the numerator anyway.

[ASunDr]

Why do you only set the numerator of the first derivative to equal zero? What if the numerator of the first derivative has no variable?

[24tdot]

so it doesn't necessarily have to pass the first derivative test in order to be a critical number?

[sueishungry]

So... finding f'(c) = undefined, but finding the undefined for the original function f(x)? Confused :((

[patrickJMT]

@sueishungry your statement confuses me

[TCOHE]

what you have taught me in less than five minutes saved me from a day of class in college calculus, you are the man!

[andreanwosu]

I had a question in my math textbook it was to find the critical numbers of the function for f(theta)=2cos(theta)+sin(theta­)^2, what would be the critical numbers for this

[neenie87]

I still dont understand how to do these, I have watched this video so much and still cant get it

[LivinOnDaMusic]

o.O i think i love you...you have no idea how much time you just saved me!!! THANK YOU SOOO MUCH!!!!!!

[antindian123]

Hey there! Thanks so much for the vid!!

I just have a question about critical numbers.

I have first derivative as ((x-2)^2(x+1)) / (x-2)^2

and second derivative as 1/2 + 4/(x-2)^3

In the answer, the number '2' was used as a critical pt for the second derivative (to determine concavity), since the second derivative is not defined at x=2

however, at x=2, the first derivative is also not defined, but it was not used as a critical number for the first derivative.

What am I doing wrong? thanks!

[persianpride93]

completely random, but im fascinated by how left handed people can write on white boards without smudging x)

[patrickJMT]

@persianpride93 they teach you tricks on how to do it in school if you take education classes

[EvezzDeed]

ughhhhh why are they showing funny ads on here?! i'm trying to study and am so tempted to get on impractical jokers.com. LOL! :D

[hahalala60]

Can you be my Calc teacher ? :)

[0505881328]

I wonder who does not like your vedios

I think he/she is jealous

cheers

^_^

[saniyeleenatalie]

The wonderful part in your all videos is, when we forget the use even a simple thing, you always remind us what we need to use. That makes you absolutely different than other professors.

We are so lucky generation that we have you.

[khwezi1986]

k now y would someone dislike this.

[MultiMoe91]

what do you mean by undefind? :(

[boxhouse23]

@MultiMoe91

It simply means there isn't an answer for it. You can't divide by 0.

For the reasoning, just go back to what dividing really means. It means having a certain amount of stuff, and sharing it equally amongst a certain amount of people. You can't really share equally amongst 0 people, so dividing by 0 is undefined.

[98hahelos]

if you would do algebra on youtube, i'll give you my soul to the lochness monster.

[cheboo12]

God bless you!

[Tripp393]

THANK YOU SO MUCH!

[GoBaltimoreOrioles]

do you have to simplify the derivative down?

[royakama]

hahaha i dont want to talk shit but it was just funny how he sais that "c in in the domain of f(x)" hahaha funny..

[migg137]

My calculus teacher sucks..... i learned in about 5 mins... something that i thought was hard.... sorry teachers but some of yall are not good

[whatever1234312]

Where the heck do I find the domain??

[christianfezeu]

hey patrick my name is christian and i was wondering how would you find the critical number of f(x)= x^3-lnx^2 please respond as soon as possible

[allawiallah]

okay so i found the critical points for a function, and then it asks for the x and y intercepts. do you know how to find that?

btw extremely generous to put all of these videos on youtube! thank you!

[CHARACTERK19]

@patrickJMT how can i know that c is in the domain?

[CHARACTERK19]

@CHARACTERK19 never mind ... i got it.

[nicknamepeach]

hi. you've been a big help to me. i was wondering do you have videos about inflection point? it's just that i can't find any, or may be there is but what are the keywords to be used to might actually find it? btw, thank you so much. you are my hope in passing calculus. :)

[kc243243]

good job!

[changez07]

thanks

[gastar1000]

bullshit. where 's the domain of the function ? following a b ook everyone does

[zachshult12345]

your a beast. thank you.

[hahaepik]

Thank you so much Patrick...

U saved my life with this amazing tutorial video ^^

[dassix1]

Thank you patrick. What makes your vidoes especially good is how neat and clean your work is, in comparison to the rest of the videos floating around youtube. Thank you for all your work.

[circasurvive04]

you're a life saver!

thank you soooo much

[BboyKundei503]

by the way, thanks for sharing. This was VERY helpful and most informative. _peace_

[MsStarwanderer]

I'm not complain because I still understood what you did, but you took the derivative of the denominator twice and the numerator not at all.

[Derelictos]

he did it right, look again. derivative of the top is 2x as is the derivative of the bottom.

[ScotleCyphez]

@MsStarwanderer the derivative of the numerator and the denominator are the same. 9 is a constant and the derivative of a constant is zero. in both cases that means you are left with the derivative of x^2, which is 2x --- hope that helps

[patrickJMT]

very few teachers are over paid

[BboyKundei503]

@patrickJMT That is true, I was making a crude reference to Professors who prioritize the "status" of their position over their students' education. Don't get me wrong. I've met some awesome instructors, but it seems so many from big & prestigious universites don't make the greatest efforts to connect with their students. The just like to hear themselve talk.

[Andyterranbase1]

@patrickJMT teachers are paid what tax payers can afford to pay them, if that means they're underpaid they should switch careers, nothing is stopping them from doing so.

[patrickJMT]

@Andyterranbase1 thank you for pointing out the obvious.

[Tripp393]

@Andyterranbase1 so you're advocating them to leave your ass to know nothing and just get another job. instead of stick with the bad pay and teach you? for you they should.

[Andyterranbase1]

@Tripp393 I'm advocating free market economics, they know what they're going to get paid before education, they choose to teach anyway, in conclusion it's not my fault they get paid 50k to teach high school + benefits and a 3 month summer vacation... If teachers didn't exist i would simply learn the material myself, it is however the 21st century.

[Tripp393]

@Andyterranbase1 "they know what they're going to get paid before education, they choose to teach anyway, in conclusion it's not my fault they get paid 50k to teach high school + benefits and a 3 month summer vacation" In that one sentence you first say they should know better than to be a teacher because of the crappy wage and then you say they shouldn't complain since they have great wages. You're an idiot, and in need of a teacher.

[franiel2323]

@BboyKundei503 i dont think you know what your talking about...

[13Nog]

How do I find the critical numbers of y = [e^(1/x)] / x^2 ? I just don't know how to do it. 0 is not in the domain, therefore can't be a critical number. Right?

[flippydoll]

I like your 'conversational' way of teaching :) the problem with my prof is, she is too-- "formal" with the way she explains that it is no longer understandable.

It also makes you want to sleep in her class!! :|

[mincemeatnme]

Question: So does it mean that points of asymptotes and holes are not considered critical numbers since they do not exist in the original function, while jump discontinuity is considered a case of critical number (UND) because it exists in the function???

[onixz100]

I can't see anything, you're a left hander and it's blocking what you're writing *cries*.

[heyyhowyadoin]

try pausing the vid

[keetner]

I have 4x-7sinx. I took the derivative of it and I ended up getting 4-7cos(x). But exactly how would we find the critical numbers...? I'm guessing you would manipulate it so it'd look like cos(x)=4/7

If anyone could help, I'd greatly appreciate it :0

Thanks!

[neogurl11]

low d high minus high d low over low squared low low low  our teacher makes us sing from her calculus the musical cd

[EmmaTheHurdler]

So helpful, way better than my teacher. I can understand this easily and it's very clear.

[darksahara8993]

Thank you very very much. I was reading my text book for about an hour and didnt understand what I had to do it was complicated I was like wth! >:O ... but n.e ways thank you so so so much again.

[iveseenspikynorman]

Thank you! Thank you! Thank you! You've accomplished what my AP teacher, and tutors/friends could not!

[genegene009]

these things give me headaches. -_- THANKS FOR THIS SIR! helped alot. got my third departmental exam today, still reviewing with you. :))

[marcusjhung]

nice, this taught me something i didnt know before.

[greencoveredbridge]

QUESTION-

So, by definition, the critical number c, plugged into the derivitive, is undefined (or zero). But when the same number, when plugged into the original equation, is undefined, then it's NOT a critical number??????

[patrickJMT]

if you find values that make the derivative zero or undefined but those same values are NOT in the domain of the original, those numbers are NOT considered critical numbers.

[MetallicaRepublic]

@patrickJMT

what do you mean by not in the domain of the original?

[Grobannela]

This video on your website doesn't work:

"Using the First Derivative to find where a funtion is increasing/decreasing and where the local maximums and minimums - Harder Example"

[patrickJMT]

yes, i need to delete that link

[patrickJMT]

KhanAcademy makes the only other vids on YouTube that i think are at all very good - the guy saul does a great job i think.

however, i do not like his crappy computer graphics : )

give me old school pen +paper/whiteboard any day! : )

he is doing great work though

[Grobannela]

I agree.He needs to change that..

but both of you are really good..And really helpful.

[tony225]

Haha. Yeah they are both very good. I think Patrick focuses a little more on really try to make things as simple and methodical as possible.

[RadoAller]

WOW,,,this is wayyyyy better then my 50min lecture,,,with a crazy maniac teaching to the board!!

[sullivanseven]

You are the father of helping people on math through youtube :P :) thanks

[patrickJMT]

i did not want any kids, and now i have millions : )

[amrita1989]

THANK YOU so much! i am no longer stressed about this.

[patrickJMT]

no problem!

[Kbrown666]

i'll have a test next monday, so this will HELP A LOT! THANK YOU THANK YOU SO MUCH!!

[keuriqueen12]

Hey, first of all, I just wanna say that your videos are awesome! They helped me loads whenever I fell asleep in my calc class. =]

But, in this video the critical numbers SHOULD include positive and negative 3 along with 0. In my calc book it says that the Definition of Critical Number is: "Let f be defined at c. If f'(c)=0 or if f' is undefined at c, then c is a critical number."

Let me know if I misunderstood this whole thing. Thanks~

[patrickJMT]

yes, you left out the part that to be a critical number, that value has to be in the domain of the original function, so +3 and -3 SHOULD NOT, SHOULD NOT be called critical numbers... so read your def'n a bit closer : )

[patrickJMT]

it is a super common mistake though

[noartificialflavor]

i wish i had discovered these videos earlier in the semester! Thankyou so so so much!

[patrickJMT]

well, what is the domain of a function?

[UhTheeNuh89]

how can you tell that positve and negative 3 are not in the domain of the original function?? is it because when it is undefined then that's how you know that it isn't in the domain of the original?? my mind is boggled =(

[sakuranbo888]

cuz, if u graph it out, u will c that at 3 & -3 there are asymptotes, but the slope doesnt change.

[SPBigJoe]

I love your videos they are a great help when my professor doesnt explain something well and rushes over it. I was just wondering, isnt it faster to use the chain rule to differentiate the function rather than the quotient rule, or are you just using the quotient rule in case viewers dont understand the chain rule?

[patrickJMT]

ha! i am glad you think so.... some people might disagree with the latter statement : )

[Cervy18]

I may not be understanding this right, but why do we take the time to even look for where the function is undefined, if any answers are never going to be in the domain?

[patrickJMT]

answers to what though? we are just sketching! and when sketching, you would want to know where the function is undefined, or your graph would be wrong

[Cervy18]

I guess what I meant was if you are JUST looking for critical numbers in a function, not sketching it, is it still necessary to find where the function is undefined since those numbers are not going to be in the domain of the function?

[galeontiger]

Excellent video as usual Patrick.

[SimplifiedQuestion]

I love your videos! You make my theoretical mathcourses so much easier! thanks alot!

[duderino987]

thanks...better than my teacher!

[brco2003]

Does this mean that any rational polynomial doesn't have a critical number, c, such that f(c) is undefined?

[patrickJMT]

correct! all critical numbers for polynomials will come from setting the derivative = 0. nothing makes a poly undefined!

[roywilliams61]

I just want to be the second one to comment,lol. Good videos BTW. :)

[Waranle]

Thank you alot!