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

question 158

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) \(c_{1}=\pm \frac{1}{10}\) , \(c_{2}=\pm \frac{3}{10}\)

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