Answer
See the proof.
Work Step by Step
Using the mean value theorem there exist $c\in (-b,b)$ such that:
$$f'(c)=\frac{f(b)-f(-b)}{b-(-b)}$$
Since $f$ is odd it follows that $f(-b)=-f(b)$ so:
$$f'(c)=\frac{f(b)+f(b)}{b-(-b)}=\frac{f(b)}{b}$$
Calculus 8th Edition
by Stewart, James
Published by
Cengage
ISBN 10:
1285740629
ISBN 13:
978-1-28574-062-1
Chapter 3 - Applications of Differentiation - 3.2 The Mean Value Theorem - 3.2 Exercises - Page 220: 30
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