# Question 12f8c

Apr 7, 2017

$\frac{\pi}{3}$. $\pi$, and $\frac{5 \pi}{3}$, if you meant to leave out the $0$. If you want all the critical numbers on a full period, then include $0$ or $2 \pi$.

#### Explanation:

$f ' \left(x\right) = 2 \sin x \cos x - \sin x = \sin x \left(2 \cos x - 1\right)$

f'(x) is nevern undefined and

$f ' \left(x\right) = 0$ at

$\sin x = 0$ or $\cos x = \frac{1}{2}$.

This leads to solutions $x = 0$, $x = \pi$, $x = \frac{\pi}{3}$ and $x = \frac{5 \pi}{3}$