Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 1 - Functions and Their Graphs - Section 1.3 Properties of Functions - 1.3 Assess Your Understanding - Page 75: 56

Answer

See graph, local maximum $f(0)=0$, local minima $f(-0.71)=-0.25$ and $f(0.71)=-0.25$, increasing on $(-0.71,0), (0.71,2)$, decreasing on $(-2,-0.71),(0,0.71)$.

Work Step by Step

Step 1. See graph for $f(x)=x^4-x^2$, Step 2. We can find a local maximum $f(0)=0$, local minima $f(-0.71)=-0.25$ and $f(0.71)=-0.25$, Step 3. the function is increasing on $(-0.71,0), (0.71,2)$, decreasing on $(-2,-0.71),(0,0.71)$.
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