Determine Whether Rolle's Theorem Can Be Applied to the Function $f ( x ) = ( x - 5 ) ( x - 6 ) ( x - 7 )$

question 16

Multiple Choice

Determine whether Rolle's Theorem can be applied to the function $f ( x ) = ( x - 5 ) ( x - 6 ) ( x - 7 )$ on the closed interval $[ 5,7 ]$ . If Rolle's Theorem can be applied, find all numbers $c$ in the open interval $( 5,7 )$ such that $f ^ { t } ( c ) = 0$ .

• A)Rolle's Theorem applies; \(c = 5 + \frac { \sqrt { 3 } } { 3 }\)
• B)Rolle's Theorem applies; \(c = 6 + \frac { \sqrt { 3 } } { 3 }\)
• C)Rolle's Theorem does apply; \(c = 7 - \frac { \sqrt { 3 } } { 3 }\)
• D)Rolle's Theorem applies; \(c = 6 + \frac { \sqrt { 3 } } { 3 } , 6 - \frac { \sqrt { 3 } } { 3 }\)
• E) Rolle's Theorem does not apply

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