Calculus, 10th Edition (Anton)

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

Chapter 3 - The Derivative In Graphing And Applications - 3.1 Analysis Of Functions I: Increase, Decrease, and Concavity - Exercises Set 3.1: 12

Answer

$\text{False}$

Work Step by Step

A function can have a positive derivative (be increasing) at one point, but whether the function is increasing on an interval requires more information. As a counterexample, $f'(1)$ is greater than 0 for $f(x)=(x-0.5)^{2}$, but at $x=0$, the function is decreasing.
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