Mean value theorem | Existence theorems | AP Calculus AB | Khan Academy

The Mean Value Theorem states that if a function f is continuous on the closed interval [a,b] and differentiable on the open interval (a,b), then there exists a point c in the interval (a,b) such that f'(c) is equal to the function's average rate of change over [a,b]. In other words, the graph has a tangent somewhere in (a,b) that is parallel to the secant line over [a,b]. Created by Sal Khan.
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AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.
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[@JD-cy2qh]

First watching all the basics here, then move to the organic chem to learn how to apply it

[@mohamedroshdy6756]

+1

[@ruby-oo9fi]

What how

[@laveyactress9647]

Loool that is exactly what i do😂😂😂❤️

[@tundeoriyomi1186]

Did same😂😂

[@delusionalplatonist6077]

it more applicable in biology tho ;)

[@DBPCINC]

37 undifferentiable functions disliked this

[@nexus_1367]

204 people liked this video but unlit 150 disliked the video🤔

[@chiragdalwani4422]

@Arid Sohan No -___-

[@chiragdalwani4422]

@Arid Sohan There is some function that has a sharp bend. They are continuous but not differentiable at the bend. Like modulus function is continuous but not differentiable at f(x)=0

[@abdelrahman914]

@Arid Sohan f(x)=|x|, f(x)=sqrt(x)...

[@lun4r16]

@Arid Sohan Sharp point. All differentiable functions are continuous is what you're thinking of.

[@geekbuddy4]

I love the way Sal explains concepts intuitively :)

[@draculiciouscoffinlove7122]

you see why and how they got the formula you are using the f(b)-f(a) / b-a is all good and makes sense y2-y1 / x2-x1 basic slope formula but he makes you really see where its from so you can understand what to do and not memorize the formulas and what to do and when to use them and in what order. i think strictly in a visual manner. i've been using khan academy all through high school and even now in college

[@alexmorgan1124]

These 7 minutes have been more helpful than all of last week in class

[@Ureyeuh]

When you see that Sal is using his thinner pen setting and the audio is nice and full: *HELL YEAH!*

[@tjboyte]

As a homeschooler who learned math thru Sal and is now reviewing for Calc final, I felt this on a personal level!

[@ashnakamura2411]

Hi, do you know which pen tablet he uses?
Thanks

[@shira966]

Honestly, this channel saved my life. You explain everything so well. Thank you.

[@ahmad32ize]

I Aced my class thanks to you SAL, I really appreciate it!!

[@thunderhead79]

"Let's calculate let's calculate let's calculate"

[@sobusbhaskor7185]

Jmund97

[@implicit2656]

Perfect!! #SalKhanForPresident!

[@nickrascona5123]

These are the people that need to be hired as professors, not researchers who don't know how to teach a class of intro calculus undergrads.

[@Tuopbc]

"our change in Y , our change... in Y, our change in Y"

[@benilginocchio]

I cannot possibly thank you enough for how intuitively this explanation is.

[@ChukapiMagnetar]

Sal, I officially nominate you the god of math teachers...

[@molbie07]

hey man i just found your channel and all i can say is you are awesome! :D
particularly after watching this video about the differential you make it seem as it should be..simple..i believe if you showed that to all highschool-university students they would understand it better than from their professor!!keep up the good work!!

[@anthonygreeko4309]

Great explanation, only thing is that you failed to mention that since the slopes are the same, the tangent line, and the secant line are parallel. Other than that, thanks for another good video!

[@fahralyacoub8970]

One thing im not able to understand is why do we use the open interval to describe the differentiability.
How would it hurt if we included a,b?

[@sonixmakeer3700]

As far as your explanation is concerned, it is really very incredible.

[@lancelofjohn6995]

The introduction makes things easy

[@Ureyeuh]

The audio in this one is GREAT!

[@hanch96]

thank you!!

[@jaiso434]

my lecturer just woke up from a bad sleep, that's how he teaches.

[@lina_a__lz]

Finally i understand this 🎉

[@araradsarkissian2859]

Perfect explanation Thank you!!! :)

[@mahakjauhri6759]

Can you explain me the reason behind considering differentiable on open interval (a, b) ?

[@stickmanbattle997]

Because if (a,b) is not differentiable even the (a,b) is continuous you can't apply the mean value theorem because for some point is not differentiable it means for a < c < b
f'(c) ≠ (f(a)-f(b))/(a-b)

[@riteshghorpade_rmg]

Why the function has to be differential over (a,b) and not [a,b] ?

[@carlosal1015]

Because by definition of derivative, a differential function on a particular point, I mean that the existence of this limit must equal both the left and the right (theory of limits), I mean that in an open interval can analyze the derived, but not on a closed interval. All differential function must meet limf (x) x to a = f (a). In a closed interval can not analyze whether the lateral limits verified. Greetings from Peru

[@raym984]

Simply put, you cannot find the derivative of an endpoint.

[@victorserras]

Khan Academy is good to get an intuitive sense about conceps but don't rely on intuitive sense alone. You need the formal and rigorous understanding of Calculus theorems too, otherwise you'll still get stuck when facing actual problems.

[@Rocky-me5cw]

What are books for?

[@heather-wong]

how does he draw his lines so perfectly straight

[@shifagoyal8221]

Excellent interpretation.

[@wavyks2159]

Helped so much! By far the best video lol

[@bushranaheed7531]

‘ The y value is ofcourse f(b).... f(b)...f(b)...’

[@jaimaa1512]

really beautiful and simple

[@farhansadikabtahifh-6158]

Thank you so much

[@MrBorchersMaths]

So helpful!! Thank you!

[@ashleyjones2691]

Clutch

[@awakenbeast9222]

6 minute taught me better than 40 minutes in class.

[@andrija_mihalic]

Thank you!

[@SnehApM06]

Thank you😍

[@bcnicholas123]

i mean that's great, but what's it used for

[@robbyburns5822]

Here's a question on my review: "Given that f(x)=x^3 find all values of x in the interval (-1,1) that satisfy the MVT"

[@spacefertilizer]

It’s used in a lot of other proofs, in my experience. There’s probably a lot of applications in physics I guess.

[@M6BrokeMe]

@@robbyburns5822 Yeah. I wonder that too. If you can take the derivative, the you already know so much more about the function than just it's average rate of change.

[@yashuppot3214]

Proving FTC without hairy epsilon and deltas.

[@Naman-sh4dw]

amazing

[@dv7551]

3:37 I'm dying

[@lansonrandell253]

so helpful!!!!!

[@vinitchauhan973]

Thank you

[@toyosisaint5214]

Explicit ❤

[@ikemoon127]

Just one more day... One more hour, one more minute, one more second, one more life...

[@mangocake8593]

111 undifferentiable functions disliked this

[@masonp5]

good video

[@andrewkaler7340]

Who else is here the night before their cal exam?

[@TheAmazingCupcake]

me! but the night before the night before xd love Sal and his videos!

[@danielle3586]

how do I know if it’s continuous or differentiable

[@sharukun]

If the tangent is always the secant,,,, I guess

[@shivanijha2607]

Is there any coaching for net csir maths??

[@PoojaSharma-wq1ni]

What is meaning of the theorem ? Eassy language definition.

[@darkvenomz9073]

Can anybody tell me why the tangent is taken in open interval (a,b)?

[@ethanvanvliet7900]

You can’t find a derivative on the end point, it makes sense bc if a derivative is slope and function is ending it’s slope no longer exists before or after it ends

[@vanizaalimerchant6252]

how is this diff then rolle's theorem?

[@ivangoncharuk607]

the slope is 0

[@flyin5952]

VanizaAli Merchant Rolle’s Theorem only applies when f(a) = f(b) so like the endpoints have the same y, I think?

[@saifalikhan5206]

You sound like Benedict Cumberbatch !

[@user-es2tw1yq4i]

what i am surprised is now i can hear what they're saying by English at the speed of 1.75
wow ! after 10 times watching video

[@funjunk2835]

DJ Vlad makes math videos?

[@namanchhibbbar2205]

i need a mathematical proof, not geometrical
its very easy to prove with geometry

[@zachsaklad5696]

@alysontina :(

[@hammadkhan5610]

i am confusion

[@nitishrajpoot5174]

Sir hindi me video bno please 🥺🥺

[@tgangster11]

use a ruler bruh

[@TheNpelletier]

5:35 And some don't

[@naturelover4141]

Kuch samjh Ni aaya

[@stamatismoraitis4986]

panelele 2020 :)

[@shehlamaryam3652]

👍👍

[@suryaprakashrobertsganj]

Please see. video on youtube

[@julixnsanchez]

what :o

[@usman5954]

👍

[@TightPancakes]

Please stop repeating a certain word or phrase over and over again. Thank you.

[@lowkeyleanin]

Then dont watch and f off

[@abdullahiahmedmohamed3925]

weak explanation

[@TimGabe1992]

Make a better video.

[@Peter_1986]

+Abdalla Axmed
"Weak"?
It cannot get more concrete and straightforward than this.

[@lowkeyleanin]

Okay abdalla. We get it. You're overqualified.

[@theCriticalEye96]

thank you!!!