Answer
$$
True.$$
Work Step by Step
True, if the relative maximum of $ f $ is $ x = 1 $, then the first derivative is zero $ x = 1 $, or the function is not differentiable at $1= x $. This means that $ 1= x $ is a point Critical for $f$.
Calculus, 10th Edition (Anton)
by Anton, Howard
Published by
Wiley
ISBN 10:
0-47064-772-8
ISBN 13:
978-0-47064-772-1
Chapter 3 - The Derivative In Graphing And Applications - 3.2 Analysis Of Functions II: Relative Extrema; Graphing Polynomials - Exercises Set 3.2 - Page 205: 16
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