Determine Whether Rolle's Theorem Can Be Applied to the Function $f ( x ) = \cos \pi x \text { on }$

question 36

Multiple Choice

Determine whether Rolle's Theorem can be applied to the function $f ( x ) = \cos \pi x \text { on }$ the closed interval $\left[ - \frac { 1 } { 2 } , \frac { 1 } { 2 } \right]$ . If Rolle's Theorem can be applied, find all numbers $c$ in the open interval $\left( - \frac { 1 } { 2 } , \frac { 1 } { 2 } \right)$ such that $f ^ { t } ( c ) = 0$ .

• A) Rolle's Theorem applies; \(c = 0\)
• B) Rolle's Theorem applies; \(c = - \frac { 1 } { 4 } , \frac { 1 } { 4 }\)
• C) Rolle's Theorem applies; \(c = 0 , - \frac { 1 } { 4 } , \frac { 1 } { 4 }\)
• D) Rolle's Theorem applies; \(c = \frac { 1 } { 4 }\)
• E) Rolle's Theorem does not apply.

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