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.

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-cyqh]

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

[geekbuddy]

I love the way Sal explains concepts intuitively :)

[alexmorgan]

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

[DBPCINC]

37 undifferentiable functions disliked this

[Ureyeuh]

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

[shira]

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

[ahmadize]

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

[thunderhead]

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

[benilginocchio]

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

[molbie]

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!!

[Tuopbc]

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

[nickrascona]

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.

[anthonygreeko]

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!

[sonixmakeer]

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

[ChukapiMagnetar]

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

[fahralyacoub]

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?

[mahakjauhri]

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

[riteshghorpade_rmg]

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

[wavyks]

Helped so much! By far the best video lol

[jaiso]

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