Question

Sketch the graph of a function f with the following properties:

f is continuous and defined on R;

f has critical points at x = −3, 0, and 5;

f has inflection points at x = −3, −1, and 2.

Short answer

Graph is :

Step-by-step solution

Step 1. Given information 

We have been given the following properties of a function f:

f is continuous and defined on R;

f has critical points at x = −3, 0, and 5;

f has inflection points at x = −3, −1, and 2.

We have to sketch the graph of this function.

Step 2. Sketch the graph

For critical points :

$f^{\mathrm{\prime }}(-3)=0;f^{\mathrm{\prime }}\left(0\right)=0;f^{\mathrm{\prime }}\left(5\right)=0$

For inflection points :

$f^{\prime \prime }(-3)=0;f^{\prime \prime }(-1)=0;f^{\prime \prime }\left(2\right)=0$

Thus, the graph is: