The Function $f(t)=\sin ^{2} 2 t$ Satisfies the Hypotheses of Rolle's Theorem on the Interval

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) $0, \frac{\pi}{4}$