Verify That the Function Satisfies the Three Hypotheses of Rolle's $f(x)=\sin 5 \pi x$

Multiple Choice

Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. $f(x) =\sin 5 \pi x$ , $\left[-\frac{2}{5}, \frac{2}{5}\right]$

A) None of these
B) $c_{1}=\pm \frac{1}{10}$ , $c_{2}=\frac{3}{10}$
C) $c_{1}=-\frac{1}{10}$ , $c_{2}=\pm \frac{1}{10}$
D) $c_{1}=\frac{1}{10}$ , $c_{2}=\pm \frac{3}{10}$
E) $c_{1}=\pm \frac{1}{10}$ , $c_{2}=\pm \frac{3}{10}$