The Function $f ( t ) = \sin ^ { 2 } 2 t$

Multiple Choice

The function $f ( t ) = \sin ^ { 2 } 2 t$ satisfies the hypotheses of Rolle's Theorem on the interval $\left[ 0 , \frac { \pi } { 2 } \right]$ . Find all values of $c$ that satisfy the conclusion of the theorem.

A) 0
B) $\frac { \pi } { 4 }$
C) $0 , \pm \frac { \pi } { 4 }$
D) $0 , \frac { \pi } { 4 }$