CALCULUS Understanding Its Concepts and Methods

Cauchy's mean value theorem

Cauchy's mean value theorem is a generalization of the mean value theorem that looks at two functions instead of just one:

If
*f*
and
*g*
are functions that are

**1.**continuous
on the closed interval
[*a*, *b*],
and

**2.**differentiable
on the open interval
(*a*, *b*),

then there is a number
*c *in
(*a*, *b*)
for
which

The theorem is named after Augustin Cauchy (1789--1867).

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Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.