Calculus: Early Transcendentals 8th Edition

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

Chapter 4 - Section 4.3 - How Derivatives Affect the Shape of a Graph - 4.3 Exercises - Page 301: 25

Answer

(a) $f'(x) \gt 0$ for all $x$, so the graph is increasing. $f''(x) \lt 0$ for all $x$, so the graph is concave down. (b) $f'(x) \lt 0$ for all $x$, so the graph is decreasing. $f''(x) \gt 0$ for all $x$, so the graph is concave up.

Work Step by Step

(a) $f'(x) \gt 0$ for all $x$, so the graph is increasing. $f''(x) \lt 0$ for all $x$, so the graph is concave down. (b) $f'(x) \lt 0$ for all $x$, so the graph is decreasing. $f''(x) \gt 0$ for all $x$, so the graph is concave up. We can see the graphs below:
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