Chapter 4 - Applications of the Derivative - 4.2 What Derivatives Tell Us - 4.2 Exercises - Page 258: 90

See the graph.

The graph sketched must be concave up on $(−∞,−2)$ and on $(4,∞)$, and must have a flat tangent line at $x = −1$, $x = 1$, and $x = 3$. A convenient way to ensure that $f(−2) = f(2) = 0$ is to have inflection points occur there. The example to the right is only one possible such graph.