Calculus 8th Edition

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

Chapter 3 - Applications of Differentiation - 3.3 How Derivatives Affect the Shape of a Graph - 3.3 Exercises - Page 227: 5


Increasing on $(1,5)$ and decreasing on $(0,1) U (5,6)$ Local maximum at $x=5$ and local minimum at $x=1$

Work Step by Step

Refer to the graph, which is a graph of $f'(x)$ When the derivative is positive, $f(x)$ is increasing. $f'(x)$ is positive on $(1,5)$ When the derivative is negative, $f(x)$ is decreasing. $f'(x)$ is negative on $(0,1) U (5,6)$ Local maxima occur when the derivative goes from positive to negative (crosses the x axis from top to bottom). This occurs at $x=5$ Local minima occur when the derivative goes from negative to positive (crosses the x axis from bottom to top). This occurs at $x=1$
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