Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 1 - Section 1.3 - More on Functions and Their Graphs - Exercise Set - Page 200: 133


This statement does not make any sense.

Work Step by Step

Consider the fact that the graph decreases in an interval $\left( -\infty ,a \right)$ and increases in an interval $\left( a,\infty \right)$. This means that the point $a$ is a critical point as after that point the nature of the graph is changed from decreasing to increasing. This implies $f\left( a \right)$ is not a relative maximum. If the graph is decreasing on $\left( -\infty ,a \right)$ and increasing on $\left( a,\infty \right)$ , then $f\left( a \right)$ must be a relative minimum. Hence, this statement does not make any sense and $f\left( a \right)$ is a relative minimum.
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