Determine Whether Rolle's Theorem Can Be Applied to the Function $f ( x ) = x ^ { 2 } - 2 x - 3$

question 47

Multiple Choice

Determine whether Rolle's Theorem can be applied to the function $f ( x ) = x ^ { 2 } - 2 x - 3$ on the closed interval $( - 1,3 )$ . If Rolle's Theorem can be applied, find all values of $c$ in the open interval $( - 1,3 )$ such that $f ^ { t } ( c ) = 0$ .

• A) Rolle's Theorem applies; \(c = 1\)
• B) Rolle's Theorem applies; \(\mathrm { c } = 2\)
• C) Rolle's Theorem applies; \(c = 0\)
• D) Rolle's Theorem applies; \(c = - 1\)
• E) Rolle's Theorem does not apply

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