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 4 - Exponential and Logarithmic Functions - Section 4.1 Composite Functions - 4.1 Assess Your Understanding - Page 281: 86

Answer

See graph, maximum $f(1.15)=1.08$ at $x=1.15$, minimum $f(-1.15)=-5.08$ at $x=-1.15$, increasing on $(-1.15,1.15)$, decreasing on $(-3,-1.15),(1.15,3)$.

Work Step by Step

Step 1. See graph for $f(x)=-x^3+4x-2$ over $(-3,3)$. Step 2. We can find a local maximum $f(1.15)=1.08$ at $x=1.15$, a local minimum $f(-1.15)=-5.08$ at $x=-1.15$, Step 3. We can determine the function is increasing on $(-1.15,1.15)$, decreasing on $(-3,-1.15),(1.15,3)$.
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