Verify That the Function Satisfies the Three Hypotheses of Rolle's $c$

question 132

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) \(c _ { 1 } = \pm \frac { 1 } { 10 } , c _ { 2 } = \pm \frac { 3 } { 10 }\)
• 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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