Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 2 - The Derivative - 2.2 The Derivative Function - Exercises Set 2.2: 29

Answer

False.

Work Step by Step

If a function is differentiable at a point, it must be continuous at that point. However, the converse is not true. A counterexample would be finding the derivative at $x=0$ for $f(x)=|x|$. The function is continuous at $x=0$, but there is a "pointy spot", so the derivative must not exist.
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