Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 4 - Section 4.1 - Maximum and Minimum Values - 4.1 Exercises - Page 284: 64

Answer

The critical numbers are: $x = -2.1$ $x = -1.3$ $x = -0.2$ $x = 1.3$ $x = 2.3$
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Work Step by Step

$f(x) = \vert 1+5x-x^3 \vert$ On the graph we can see two local maxima where $f'(0) = 0$ Using the zoom function on a graphing calculator, we can estimate that these two critical numbers are $x = -1.3$ and $x = 1.3$ On the graph we can see three points which meet the x-axis at sharp points. At these three points, $f'(x)$ is undefined. Using the zoom function on a graphing calculator, we can estimate that these three critical numbers are $x = -2.1, x = -0.2,$ and $x = 2.3$
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