CALCULUS Understanding Its Concepts and Methods

Mean value theorem

Mean value
theoremLet
*f*
be a function having the properties that

**1. ** the function *f*(*x*)
is continuous for *a ≤ x ≤ b* and

**2. ** the derivative *f'*(*x*)
exists for *a < x < b*.

Then there is a number
*c*,
with
*a < c < b* ,
for
which

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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.