Verify That the Function Satisfies the Three Hypotheses of Rolle's $$f ( x ) = \sin 5 \pi x , \left[ - \frac { 2 } { 5 } , \frac { 2 } { 5 } \right]$$

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) $c _ { 1 } = \pm \frac { 1 } { 10 } , c _ { 2 } = \pm \frac { 3 } { 10 }$
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) None of these

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