Answer
$f(x)$ is not differentiable at $x=0$
Work Step by Step
Given $$f(x)=(x-1)|x|, \quad a=0$$
From the following figure, we have a sharp corner at $x=0$. Thus, $f(x)$ is not differentiable at $x=0$ (no tangent line exists there).
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 - 3.2 The Derivative as a Function - Exercises - Page 116: 77
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