Determine the Relative Extrema of the Function $y = 2 \cos x + \sin 2 x$

Multiple Choice

Determine the relative extrema of the function $y = 2 \cos x + \sin 2 x$ on the interval $( 0,2 \pi )$ .

A) relative minimum: $\left( \frac { 5 \pi } { 6 } , \frac { 3 \sqrt { 3 } } { 2 } \right)$ relative maximum: $\left( \frac { 5 \pi } { 6 } , - \frac { 3 \sqrt { 3 } } { 2 } \right)$
B) relative minimum: $\left( \frac { 5 \pi } { 6 } , - \frac { 3 \sqrt { 3 } } { 2 } \right)$ relative maximum: $\left( \frac { \pi } { 6 } , \frac { 3 \sqrt { 3 } } { 2 } \right)$
C) relative minimum: $\left( \frac { \pi } { 6 } , - \frac { 3 \sqrt { 3 } } { 2 } \right)$ relative maximum: $\left( \frac { 5 \pi } { 6 } , \frac { 3 \sqrt { 3 } } { 2 } \right)$
D) relative minimum: $\left( \frac { \pi } { 6 } , \frac { 3 \sqrt { 3 } } { 2 } \right)$ relative maximum: $\left( \frac { 5 \pi } { 6 } , - \frac { 3 \sqrt { 3 } } { 2 } \right)$
E) relative minimum: $\left( \frac { 5 \pi } { 6 } , \frac { 3 \sqrt { 3 } } { 2 } \right)$ relative maximum: $\left( \frac { \pi } { 6 } , - \frac { 3 \sqrt { 3 } } { 2 } \right)$