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 284: 31

Answer

Concave upward on $$ (2, \infty). $$ Concave downward on $$ (-\infty, 2). $$ The graph has no inflection points

Work Step by Step

Since the graph of the function lies above its tangent line at each point of $(2, \infty)$ . So, concave upward on $$ (2, \infty). $$ Since the graph of the function lies below its tangent line at each point of $(-\infty, 2)$ . So, concave downward on $$ (-\infty, 2). $$ Since a point where a graph changes concavity is inflection points, therefore the graph has no inflection points
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