Chapter 5 - Graphs and the Derivative - 5.3 Higher Derivatives, Concavity, and the Second Derivative Test - 5.3 Exercises - Page 284: 32

Concave upward on $$ (-\infty, 0). $$ Concave downward on $$ (0,\infty). $$ The graph has no inflection points .

Since the graph of the function lies above its tangent line at each point of $(-\infty, 0)$ . So, concave upward on $$ (-\infty, 0). $$ Since the graph of the function lies below its tangent line at each point of $(0,\infty)$ . So, concave downward on $$ (0,\infty). $$ Since a point where a graph changes concavity is inflection points, therefore the graph has no inflection points