Chapter 5 - Graphs and the Derivative - 5.3 Higher Derivatives, Concavity, and the Second Derivative Test - 5.3 Exercises - Page 283: 27

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 $(2,3).$ So, Inflection point at $$ (2,3). $$

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 $(2,3).$ So, Inflection point at $$ (2,3). $$