Answer
True.
Work Step by Step
Let $a$ and $b$ be any two x-values in the domain of $f(x).$
Using Rolle's Theorem over the interval $[a. b]\to$ $f'(x)=\dfrac{f(b)-f(a)}{b-a}\to$
$0=\dfrac{f(b)-f(a)}{b-a}=\to f(b)=f(a)\to f(x)$ is constant.
Calculus 10th Edition
by Larson, Ron; Edwards, Bruce H.
Published by
Brooks Cole
ISBN 10:
1-28505-709-0
ISBN 13:
978-1-28505-709-5
Chapter 3 - Applications of Differentiation - 3.2 Exercises - Page 176: 76
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