Finding Local Maximums/Minimums - Second Derivative Test

[xD135ELx]

I'm guessing four people dropped calculus



[SamBM17]

Hi Patrick. Where you've differentiated f'(x) so f''(x) = (x^2+4)(-2x) - (4-x^2)2 x (x^2+4)2x where does the 2 outside (4-x^2) come from? I hope my question makes sense, thanks

[citizenofvirginity]

@SamBM17 That's the derivative of the bottom of the second derivative (x^2+4)^"2" = "2"('x^2'+4)('2x'). The chain rule.

[JosiahPlummer1988]

@SamBM17

He was differentiating the denominator of f-prime. The derivative of (x^2+4)^2 is 2 * (x^2+4) * 2x. That's where the 2 came from; it's not associated with (4-x^2).

[L4ctose]

nice video, but you couldve shortened it to like 2 minutes

[patrickJMT]

@L4ctose thanks for your useful comment. it is valued and appreciated!

[Eadaoin94]

@patrickJMT I have to say I agree... but only because I have a massive test in algebra, differenciation, matrices and integration tomorrow and I'd love some fast cramming videos... but good videos!

[patrickJMT]

@Eadaoin94 better to be 2 minutes too long instead of 2 minutes too short!

[Scroowful]

It's awesome that you explain math so understandable and in the easiest way :)

[Iced0826]

Math professors really need to learn from YouTube... :">

[Bluach2]

pancakes

[Shadowrider941]

Thank you! This video has helped me so much!!! :D

[darrinjamminn360]

patrickJMT, I am passing Calculus because of you. You are awsome. Thank you so much!

[Ahmed1390]

I feel Lefties are better mathematicians than a Righties !!

[oleboy96]

@Ahmed1390 I´m a leftie!!!!

Thats motivating me alot!!!! xD

[musicalchopstics]

yay asian pens!!!

[MarMarZwinZ]

what if you get a 0 when plugging in the critical points to the second derivative?

[richindiankid]

Go to patrick's website and donate to his paypal!!

[patrickJMT]

@richindiankid that sounds like a good idea. with a name like ' richindiankid ' i hope you gave a LOT! : )

[Constantinople5]

Your videos are a life saver! I would probably be failing calculus without these videos.

[Sasha7amad]

The way you say "excuse me" is just so cutee! I hope you got over the fact that you've got some creepyy students lol

[patrickJMT]

@Sasha7amad : )

[rr5001]

how many lvls of calculus r there?

[patrickJMT]

@rr5001 1

[Constantinople5]

@rr5001 Generally, calculus is split up into 3 classes, Calculus I, II, and III. Upper division courses might include differential equation and muli-variable calculus.

[zkfinsterwald]

oh nevermind

[zkfinsterwald]

Would you plug in the values where f ' (x) is undefined into f " (x) also??

[dbrogs11]

ITS UNDER THE BLANK PAPER UNDER THE SECOND DERIVATIVE PAPER!!

[RenzGonzaga33]

im smiling so much because you helped me understand this so well...am i weird? lol

[jojogirl2008]

thanks so much! it was great like always! :)

[guitarsea003]

do you have videos wherein you apply maxima and minima to word problems? :)

[patrickJMT]

@guitarsea003 optimization problems

[guitarsea003]

@patrickJMT ohhh. thanks man! :D

[born4computer]

Why would you use such a complicated equation for a how to video?

[DJSt3v3n]

THANKS X 1000

[patrickJMT]

@DJSt3v3n no problem!

[patrickJMT]

@LucLamontCaputo well, a math phd is not easy. and i do not want it. i dont want a uni prof job

[sxswitch]

This helps a lot. I already knew how to do everything but when my teacher introduced the more than or less than zero for the second derivative, he confused me completely. This video cleared everything up.

[patrickJMT]

@sxswitch glad i could help : )

[KrhystalZz]

@patrickJMT I have a question. Ok my teacher said that nowadays AP tests require you that you state everything. Like reasons by which the function works for the certain theorem. Could you explain, if you know, which are the ones I have to state.

[thealbinohobo33]

great video. heres a suggestion though, if you could put the steps in the description it would help a lot (i.e. step 1 find derivative, 2, critical numbers, 3 plug critical numbers in)..but great video!

[LoveHateLoveHate100]

Grrr. I'm taking this in high school and my math teacher is good at explaining this, but goes too fast. -_- Thanks for the help. :) the second derivative test usually kicks my --- a lot.

[trannghi7707]

damn it why dont u just pick a easier problem with no fraction lol

[BurnedJew]

When you did the first derivative, you went from x^2+4-x(2x) over x^2+4 to -x^2+4 over (x^2+4)^2. I can't quite understand how you got that.. What happened to the x(2x)..

[3hite5tripes]

when you reduced the first derivative, what happened to the  -x(2x)???

[jpmoench21]

thanks for the help!

[rpsc06]

Why aren't you a university prof, your better than all my math profs combined!

[patrickJMT]

@rpsc06 no phd

[nellycorture]

I honestly dont understand why i even go to class anymore. It is such a waste of my time! I go for 2 hours a day to calculus learning absolutely NOTHING, then i come home and watch this 11 min video it all makes sense! Thanks for the vids, you saved my life countless times :)

[sillymonkard]

Boosh! That was hot.

[NguyenEmpir3]

@ 10:18 why did we have to plug in the 1st deriv?

[sheepmakewool]

Oh papa!

[kerpalh]

@sheepmakewool mnyes? You called?

[MultiMoe91]

can we find the local Max/MIn, using the first derivative?

[oreocookie810]

wait so both the first AND seond derivative have to be positive or negative for it to be a local minimum or maximum? not just the second derivative?

[kevinr515]

thanks so much, none of my math professors and TAs can speak clear english and this is saving my life. Kinda getting mad at youtube for ads in the middle of the video. But keep up the great work

[patrickJMT]

@kevinr515 glad to help! thanks for letting me know about the ad in the middle - it should be gone now!

[tokenblakk]

lol, you lost the page underneath that blank sheet

[TheKingstoncowboy]

You should choose an easier number to differentiate so we can understand the concept quicker. thanks though!

[shaq147]

thats sum crazy shitttt

[letthemxeatcake]

THANK YOU THANK YOU THANK YOU! I need to study this for my exams!

[patrickJMT]

@letthemxeatcake no problem, hope it helps.

[desidork000]

leftyyyy

[Mehrnaz926]

I totally agree, you do have nice hands.

[zinadine92]

im gay for you

[PengunaFilms]

YOU SAVED MY LIFE.

[KoreaXFan]

YES. you have this videooo!! I slacked off after derivatives and was falling behind in class. This will catch me up :D

[XCrystalXClearXLoveX]

hahaha, lovely singing voice!

i love your videos!! Im desperately trying to prepare for my math finals in 2 days! wish me luck :)

[flyordie2]

You make me enjoy my least favorite subject a little bit more. Thanks. :)

[MattyHild]

@ 3:14 when you are finding the critical points, how is it possible to find those points without including the denominator?

[sonicr007]

@MattyHild this was because the first derivative test only shows where asymptotes are on the denominator if its = to 0 but true it is an imaginary number because x^2=-4

[1789Mikaela]

I LOVE U!!!!!!!!!!!!!!! U R A LIFE SAVER!!!!

[IsBreadFreeHere]

"And on the bottom!!!" Hahahah that was hilarious. Math is funny

[iviriya]

thank you

[haisumabbas]

great work....................

[MrPowellw]

you are writing with the wrong hand

[SirThursday3]

@MrPowellw

What?

[Corrup7edChaos]

thanks for the help!

[1016JP1]

Very helpful, thanks man! You explain it better than my math teacher lol.

[RhymelessWater]

These videos saved my life. From a D in AP Calc BC to a B in 3 weeks. :D And now I'll be getting an A this quarter.

[TheNemeson]

You should try American Idol, might make it to LA. ^__^

[thecheese23]

PERF!!

[SCIGEEK15]

when you get to 6:06 of the video .. where do you get the 2 from?

[gyhighway]

Is it possible to get only one critical value when finding the first derivative?

[kupop0w]

@gyhighway yea

[ronanmahony1990]

hi just wondering are you finding thhe intervals of local max/min here or just the points? I'm pretty sure I need to know how to get the intervals how do i do that?

[tamtut5]

@ronanmahony1990

Find the critical points

[gsharpshooter80]

Yep.. I just failed math 161. Thanks for the help tho.

[upsidedownsoup]

Patrick, I love you. You have unknowingly helped me with math for the past 3 years now, and I feel I must say that I wish I had you as a teacher. Thank you so much man (I know you get it alot, but seriously, you rock!).

[KingEntity91]

I respect you a lot Patrick you helped out a lot! However, will the second derivative test always give you a local maximum or a local minimum? Or in other words.... if there are any, what type of function wouldn't work with this test?

[jasonsheil]

lol. It sounds like hes singing "and on the bottom!" at 07:46

[pauthewXXIV]

the lost paper is below that blank paper!! look at 10:01 hehe

what a great teacher

[CineOT]

Actually, when f''(c) = 0 (let c be a critical number) you have an inflection point. This means that the function changes it's concavity.

Good tutorial, anyway! Really nice

[illmatic33]

f(x)= -X^3-5X^2+4X-2

I am trying to: a. determine the intervals of increasing and decreasing. b. determine local min and max. c. determine the intervals of concave up and concave down. d. point of inflection.

Can someone pleeeeeze solve this problem :-( its driving me nutz!

[janitarjanitar]

AND ON THE BOTTOM!

[janitarjanitar]

OMG we have the next Justin Timberlake teachin us Calculus.. listen!!! --> 7:46

[cellophanerose]

Great video! You could have simplified the first derivative from (4-x^2) / ((x^2+4)^2) to -1 / (x^2+4) and would have bypassed a lot of algebra for the second derivative. :P Awesome explanation nonetheless and very helpful. :)

[dual85]

Use TI-89! : )

[77777computerperson]

thanks for posting

[Zeldamariomz]

heh at 10:03 is that when the paper gets lost?

[paris0818]

You are an excellent resource. I hope by reviewing your videos, I will be able to pull up my grade in calculus. It's been 30 years since precalc.

[pravin2379]

uh....

[ince4reel]

Negative x negative is Positive so the answer should be 16 at 7:45 right?

[DjGalm]

yeah man it's 16 loooool good catch... thank god it didn't alter the outcome though... it would've been a mess and the answer would be +... Patrick can you please fix this? I know it's a minor error but some people could go crazy over it.

[patrickJMT]

yes, i agree! i strive to point out minor mistakes using annotations, and simply delete vids that have more serious mistakes.

the last thing i want to do is teach someone incorrectly or make a huge, confusing mistake!

[DjGalm]

Thank you Patrick! :D My final is on this Wednesday and this particular video just unlocked the last closed door in my brain regarding the extrema.

[patrickJMT]

nothing feels better than when things start to 'click'! good luck on the final!!

i will be sending you brain waves tomorrow, so make sure you go into the test wearing some sort of tin-foil helmet that you construct yourself, or they might miss and go to someone else!

[DjGalm]

hahahaaaaaa you are halarious xD! Thank you veeerrryyyy much!!! I'm gonna be honest with you and say that I have a somewhat powerful sixth sense... I come across things/events before they happen... The only thing I can't come across is questions in an exam, not even a quiz!... I swear this is so frustrating!... I sure could use wireless info transfer directly to my brain! wooot woot! :D

[mrana14]

like it

[lilinsia100]

you have nice hands

[patrickJMT]

that is what a friend who i was perpetually in love with growing up used to always tell me : )

[WhyMustYouFail]

@patrickJMT You've probably heard this a million times already, but you are awesome.

[Mehrnaz926]

I was just thinking that.

[ZheKon]

Nice video

[jrendoso]

where is the Download button ?

[patrickJMT]

look just below the ratings (all the red stars) and to the right.

it is just below the 'run time' clock

[ulivaldo]

Put it in your favourities and you can watch it again and again

[majd2]

or top and down or , from down to top

sorry for my bad english , and thx again dude ,, and may u take ur stuff to harder lvl :):):)

---------

bad youtube dont allow me to put all the text in one coment so i devide it to 2 parts :D

[majd2]

dude i am l learn this stuff , i am from palestine 16 years old , in the teen grade , its gool to wathc ur vidoes , but this relly easy , sometime i even enjoy slove them , all we have to do is F(X)' = 0 , and found the x then back to the main proplem and found the Y Then we have the (x,y) then or we make the f(x)'' or we take point before it and after it , all u have is to understand how the draw of it will like like ,

[Mig440]

Very good explanation of a, sometimes, difficult method to understand ;)