Answer
See the graph.
Work Step by Step
$f'(x)$ is $0$ on the interior of the given interval at $x = ±3π/2$, $x = ±π$, $x = ±π/2$, and at $x = 0$. $f'(x) > 0$ on (−2π,−3π/2), and on (−π,−π/2), and on (0, π/2), and on (π, 3π/2), so $f$ is increasing on those intervals. $f'(x) < 0$ on (−3π/2,−π), and on (−π/2, 0), and on (π/2, π), and on (3π/2, 2π), so $f$ is decreasing on those intervals. There are local maxima at $x = ±3π/2$ and $x = ±π/2$, and local minima at $x = 0$ and at $x = ±π$. An example of such a function is sketched.
