Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 2 - Derivatives - 2.1 Derivatives and Rates of Change - 2.1 Exercises - Page 114: 17

Answer

$g'(0)$ < $0$ < $g'(4)$ < $g'(2)$ < $g'(-2) $

Work Step by Step

Explanation: $g'(x)$ corresponds to the slope of the tangent line at $(x, g(x))$ Looking at the graph you can see that $g'(0)$ is the only negative slope so it is the only value less than zero $g'(0) < 0 $ Looking at relative (positive) slopes of $g'(-2)$, $g'(2)$, and $g'(4)$ you can see that $g'(-2)$ has the steepest slope, $g'(2)$ has the second highest slope, and $g'(4)$ the least out of the three. $g'(4)$ < $g'(2)$ < $g'(-2) $ Thus $g'(0)$ < $0$ < $g'(4)$ < $g'(2)$ < $g'(-2) $
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