Answer
$f'(x)$
Work Step by Step
The average value of $f$ on the interval $[x,x+h]$ is:
$$\lim_{h \to 0}\frac{f(x+h)-f(x)}{(x+h)-x}$$
But this is exactly the definition of the first derivative:
$$\lim_{h \to 0}\frac{f(x+h)-f(x)}{h}=f'(x)$$
Calculus 8th Edition
by Stewart, James
Published by
Cengage
ISBN 10:
1285740629
ISBN 13:
978-1-28574-062-1
Chapter 5 - Applications of Integration - Review - Exercises - Page 394: 33
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