Answer
See the graph.
Work Step by Step
$f'(x)$ is $0$ at $x = −4$, $x = −2$, and $x = 1$. $f'(x) > 0$ on (−4,−2) and on (1,∞), so $f$ is increasing there, while $f'(x) < 0$ on (−∞,−4) and on (−2, 1), so $f$ is decreasing on those intervals. There must be a local maximum at $x = −2$ and local minimums at $x = −4$ and $x = 1$. An example of such a function is sketched.
