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Mean value theorem illustrated

Author:Tim Brzezinski

Here we illustrate the Mean Value Theorem: if a function

satisfies the two conditions

is continuous over the closed interval , and
is differentiable over the open interval ,

then there exists at least one point

in

for which

. Geometrically, the conclusion of the theorem says there exists a point

in

for which the slope of the tangent line to

at the point

is equal to the slope of the secant line through points

and

.

Developed for use with Thomas' Calculus, published by Pearson.

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