Critical points introduction | AP Calculus AB | Khan Academy

[@deborahfranza2925]

Why my professor couldn't explain this concept so concisely is a mystery to my, but thank you for creating Khan Academy. It has carried my math education in community college all the way up from pre-algebra to now Calculus 1. #Ioweyoumylife

[@ShubhamGhosh-sp8kb]

You are lepd

[@georgeb8637]

5:43-6:08 - Critical Point - explanation (what, how to find) where f'(x) = 0 or undefined 6:55-7:29 - How to find Maximum/Minimum Value #theory Not explained how to find critical point

[@sasmitamaharana2083]

U r stupid

[@sushantshah1251]

Read your comment again...

[@Nomsaday]

😭 😭 😭 😭 ​@@sushantshah1251

[@ScientificVoyage]

An explanation with exceptional clarity.

[@bilgekyran9902]

I searched all the internet to check that simple question and couldn't find it anywhere. thank you so much

[@bor3y2]

WOW I love the colors

[@ItsAmirSheidaei]

I was just thought this in my AP calculus class! Great job!

[@DacoRoo]

I'm always amazed that there is never a video that explains what I'm stuck on. Everyone recommends your videos, but they never help me.

[@shudidesai]

Dude just use Khan Academy videos, they're great.

[@vaibhavverma6847]

DacoRoo This means you get stuck in very very basic theings

[@thefirst512]

DacoRoo professor Leonard is good for math [101] [101]

[@ahmetsezginn]

Vaibhav Verma I believe it is opposite since these are pretty simple

[@legoreview8228]

Maybe because you are not destined to be a mathematician....

[@Do-Some-Change]

I'm not gonna lie when this was uploaded , I just had ended my 1st class

[@thanaa6401]

Sal this is one of the most incredible videos of yours!!!

[@muthyalakoushil7101]

In class I feel maxima and minima is sooo bore but now I feel so interesting that u so much for khan academy 😍😍😍😍😍😍😍😃😃😃😃😃😃😃😃😃

[@mikewarrior4472]

ur voice makes a lot of difference too great work

[@michaelhoefler5118]

Shouldn’t f(x0) also be a local maximum?

[@moonshiry]

Very, very, clear and simple to understand

[@MelgMike53]

2:37 -- "Not lox, that would have to deal with salmon" - I died laughing when he said that lol

[@allielee]

salmon khan

[@basitbashir2101]

Khan academy is best in the world

[@nexypointy]

thank you mr. khan!

[@amrmoneer5881]

this is great thanks sal khan

[@harnoorkaur3120]

the global maximum in the graph is also a local maximum

[@kumarhemjeet4846]

No !

[@thatoesia4353]

this is beautifull...well explained sir

[@kylenason]

So, can the global max also be considered a local max when there are points on both sides of it on the graph and interval or can it only be considered a global max?

[@havetoprove2569]

I know it's late but I think a global maxima is automatically a local maxima in its respective domain

[@fafelinabm3601]

I calculate myself just to understand it, but when you plug in f(-4) in f'(x)=2x+4, the result is negative not positive. It should be -4 not 4. At minute (2:22) in the video.

[@bellajaid]

In what video? There is no function or numbers here....

[@gauravbhandari1184]

Nicely explained

[@ginevrabianco4056]

Is it fair to say that if the derivative does not exists at a point, then this critical point can be a local min /local max?

[@wodhks1026]

what is derivative

[@CODE_CRINGE]

@Steven Yang lol I hope you are joking

[@wodhks1026]

Now I'm in Calc 3 in University and I still don't know what derivative is.

[@wodhks1026]

Now I'm a Sophomore in College and I don't know what Derivative is And I took Diff Eq and Linear Algebra Still don't know

[@melvincooly8]

It's funny seeing you grow over the years lol. I think a google search would help you :)

[@هيلة-ع8م]

Lmfao

[@MSDhoni-pz5wc]

Hello Khan sir! Sir , why can't we choose the lowest values at the end of the interval??

[@riley12c]

when u learn about salmon in a math video

[@DevashishGupta132435LC]

brilliant

[@Intrepid231]

All the video made sense, but what is x and y on the vertical and horizontal axes of this graph?

[@SaKemp01]

That just means x-axis and y-axis.

[@zuesr3277]

+SaKemp01 y = f(x).

[@p4blo90]

nice work

[@iMacBoy91]

Can a global minimum or maximum be a local mini/maxi in the meantime?

[@vaibhavverma6847]

مصطفى العبيدي nice question bro

[@MrSwaagar]

Very helpful video. :)

[@hassnataha9593]

What is relative maxima and minima

[@sitiaishah3488]

So the theorem that relates local max/min with critical points is not valid for max/ min at the end point? 😕

[@ragulponraj1196]

Why critical points are not necessarily the minimum or maximum points? Can't I just make them the min. or max. point by choosing an interval such that these points are max and min?

[@VIJAYKUMAR-xi4ow]

splendid

[@rukhiyakulsoom.m6075]

nce, thnx

[@saisrirajpasumarthy4261]

What is the difference between Global and Local Maxima? Why can't a Global Maxima in the above Function be the Local Maxima.

[@joelfeeley8122]

saisriraj p the global maximum is the highest point of the entire function. Every other turning point is referred to as local unless it’s the lowest/highest turning point.

[@janroseathena8075]

Is it possible to have 1 crit point?

[@NONAME-zf8wz]

Janrose Athena x^2?

[@Dina-hk]

what does x-naught mean? and when to use it?

[@rekhabubna9592]

why is f'(x2)not defined??please explain in detail

[@talhamohammed9541]

it's because the tangent cannot be defined at that point as it is not a well defined curve. Hope it helps:)

[@deborahfranza2925]

BY definition, tangents do not exist on corners or kinks. The derivative at those kinds of points are considered undefined.

[@udaykadam5455]

Function has to be continuously differentiable to find the tangent at each point but as you can see the condition breaks at the corners.

[@cassidyS667]

Can someone show me how to do this with trig functions?

[@TheUnknownGuy_07]

+Cassidy Scaglione trigonometric functions don t have maxima and minima

[@Z3kyTw0]

please tell me your joking

[@MATHSOLVESZONE]

Very awesome explanation!!!!!! #maximaandminima #mathsolveszone

[@kaihiwatarigaming]

Local maximum? Or local minima?

[@kaihiwatarigaming]

At 3:06

[@racheteh6157]

But why the global max cannot be local max ?

[@aadityasingh6376]

global max suppose he is the best player of the world(x) and local max be the best player in your colony (y )it can be that you live in the same colony as x and he can be the local and global maxima at the same time .

[@Nikifuj908]

Yes, but the converse is not true.

[@benkao8253]

From the side, that looks like the average free-hand curly-bracket function.

[@Summy_99]

anyone else think of liquid oxygen instead of salmon when he accidentally said "lox"

[@dheerajpadmakar1118]

sir can the background a bit more clear. i think that will be a bit more clear to understand

[@Dreadwinner]

🤯

[@samurai3939m9]

Why people call this point "critical" ?

[@satisfiction]

Sal essentially wrote "crihial points" and it bugs me. Haha.

[@jibrilmuhammadibrahimalham2389]

No he did write critical points its just that the t and i are overlapping each other ...... Lmao ...

[@dheerajpadmakar1118]

after some time it looks messy and not clear

[@Fightnight92]

These videos never help me.

[@chidriraghuveer5074]

please change your slang its like sleeping video

[@alejandrocarrizales1035]

use 1.25 speed its alot better.