Determine Whether or Not the Function $f ( x ) = \cos 2 x$

Multiple Choice

Determine whether or not the function $f ( x ) = \cos 2 x$ satisfies the hypothesis of Rolle's Theorem on the interval $\left[ \frac { \pi } { 4 } , \frac { 3 \pi } { 4 } \right]$ If it does, find the exact values of all values of $c \in \left( \frac { \pi } { 4 } , \frac { 3 \pi } { 4 } \right)$ that satisfy the conclusion of Rolle's Theorem.

A) No
B) Yes, $c = \frac { \pi } { 2 } , c = \frac { 3 \pi } { 2 }$
C) Yes, $c = - \frac { \pi } { 2 } , c = \frac { \pi } { 2 }$
D) Yes, $c = \frac { \pi } { 2 }$