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

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).

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