Answer
$h=-2$
Work Step by Step
Since
$$ \frac{f(2+h)-f(2)}{h}=0$$
Then
$$ f(2+h)-f(2)=0 \ \ \ \to \ \ \ f(2+h)= f(2)$$
From the given figure, we have $f(2)=2$, so $f(h+2)=2$, and hence $$h+2=2\ \ \to \ \ h=-2$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 3 - Differentiation - 3.1 Definition of the Derivative - Exercises - Page 103: 12
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