$\frac{1}{8} \mathrm{~cm} / \mathrm{min}$

$\frac{1}{4} \mathrm{~cm} / \mathrm{min}$

$16 \mathrm{~cm} / \mathrm{min}$

$32 \mathrm{~cm} / \mathrm{min}$

$9 \sqrt{3} \mathrm{~cm}^2 / \mathrm{s}$

$18 \mathrm{~cm}^2 / \mathrm{s}$

$6 \sqrt{3} \mathrm{~cm}^2 / \mathrm{s}$

$18 \sqrt{3} \mathrm{~cm}^2 / \mathrm{s}$

$a=50$, local minima

$a=58$, local maxima

$a=58$, local minima

$a=-50$, local maxima

Strictly increasing on $\left(\frac{3 \pi}{8}, \frac{5 \pi}{8}\right)$

Strictly increasing on $\left(\frac{\pi}{8}, \frac{3 \pi}{8}\right)$

Strictly decreasing on $\left(\frac{3 \pi}{8}, \frac{5 \pi}{8}\right)$

${\text { Strictly decreasing on }}\left(\frac{\pi}{8}, \frac{5 \pi}{8}\right)$