Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 3 - Derivatives - 3.2 Working with Derivatives - 3.2 Exercises: 1

Answer

Because the function that is positive at some $x$ can be both decreasing and increasing.

Work Step by Step

The sign of $f'(x)$ shows if the function is increasing or decreasing at that $x$. if $f'(x)>0$ then the function is increasing and $f'(x)<0$ then the function is decreasing. It doesn't matter if the function is positive at some $x$ it can be both decreasing and increasing so $f'(x)$ can be both positive and negative.
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