Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 5 - Graphs and the Derivative - 5.3 Higher Derivatives, Concavity, and the Second Derivative Test - 5.3 Exercises - Page 283: 30

Answer

Concave upward on $$ (-2, 6). $$ Concave downward on $$ (-\infty, -2) \text{ and } (6,\infty). $$ Inflection points at $$ (-2,-4) \text{ and } (6,-1). $$

Work Step by Step

Since the graph of the function lies above its tangent line at each point of $(-2, 6)$ . So, concave upward on $$ (-2, 6). $$ Since the graph of the function lies below its tangent line at each point of $(-\infty, -2)$ and $(6,\infty)$ . So, concave downward on $$ (-\infty, -2) \text{ and } (6,\infty). $$ Since a point where a graph changes concavity is $(-2,-4)$ and $(6,-1)$ So, Inflection points at $$ (-2,-4) \text{ and } (6,-1). $$
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