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

question 102

Multiple Choice

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

• A) Rolle's Theorem applies; \(- \frac { 8 } { 3 }\)
• B) Rolle's Theorem applies; \(- \frac { 8 } { 5 }\)
• C) Rolle's Theorem applies; \(- \frac { 4 } { 5 }\)
• D) Rolle's Theorem applies; \(- \frac { 4 } { 3 }\)
• E) Rolle's Theorem does not apply

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