# How do I find the numbers c that satisfy Rolle's Theorem for f(x)=cos(2x) on the interval [pi/8,(7pi)/8] ?

Find $c$ in $\left(\frac{\pi}{8} , \frac{7 \pi}{8}\right)$ to solve $f ' \left(c\right) = 0$.
Since $f ' \left(x\right) = - 2 \sin \left(2 x\right)$ this amounts to solving
$- 2 \sin \left(2 x\right) = 0$ for solutions in $\left(\frac{\pi}{8} , \frac{7 \pi}{8}\right)$