Consider a function $f(x)$, with domain $x \in [0, 2\pi]$, and derivatives given by
$f'(x) = \frac{\cos x}{\sin x - 2}$
$f''(x) = \frac{-1 + 2 \sin x}{(\sin x - 2)^2}$
Then:
$\bullet$ $f(x)$ has a local minimum at $x = $
$\bullet$ $f(x)$ has a local maximum at $x = $
$\bullet$ $f(x)$ is concave up over the interval $(…, …)$
