Mean Value Theorem

Intuition behind the Mean Value Theorem

Uploaded by: khanacademy
Tags for this video: calculus mean value theorem CC_39336_F-IF_6

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It's cool if you ... ( 6 months ago by Oboeplayer511)

It's cool if you solve this for a general quadratic; Ax^2+Bx+C for the interval [h,k]
(A(h^2)+B(h)+C)-(A(k)^2+B(k)+C))/(h-k)=2Ax+B (derivative of the general quadratic)
(A(h^2)-A(k)^2+B(h)-B(k))/(h-k)=2Ax+B
(A(h^2-k^2)+B(h-k))/(h-k)=2Ax+B
(A(h-k)(h+k)+B(h-k))/(h-k)=2Ax+B
A(h+k)+B=2Ax+B
A(h+k)=2Ax
x=(h+k)/2
so the x-coordinate for any parabola where the average slope is equal to the slope of the derivative at the point is equal to the average of the endpoints of that interval...FASCINATING

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I feels good after watching this, my lecturer definitely confused me everything about this.

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Say the interval is ... ( 1 month ago by TerminatorSe7en)

Say the interval is [a,b], can C be equal to a? or just the open interval ( A point somewhere between a and b )?

Why can't teachers ... ( 4 weeks ago by Godamie)

Why can't teachers and textbooks just explain right on the spot with simple words instead of trying to make it sound all scholarly and beating around the bush?

thank you for ... ( 1 week ago by MrCyborg29)

thank you for explaining open/closed interval