Determine whether the Mean Value Theorem can be applied to the function $f ( x ) = x ^ { 3 }$ on the closed interval $[ 0,16 ]$. If the Mean Value Theorem can be applied, find all numbers $c$ in the open interval $( 0,16 )$ such that $f ^ { t } ( c ) = \frac { f ( 16 ) - f ( 0 ) } { 16 - 0 }$.
A)
MVT applies; $- \frac { 16 \sqrt { 3 } } { 3 }$
B) MVT applies; 4
C) MVT applies; $\frac { 16 \sqrt { 3 } } { 3 }$
D) MVT applies; 8
E) MVT does not apply

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The Answer of Determine whether the Mean Value Theorem can be applied to the function $f ( x ) = x ^ { 3 }$ on the closed interval $[ 0,16 ]$. If the Mean Value Theorem can be applied, find all numbers $c$ in the open interval $( 0,16 )$ such that $f ^ { t } ( c ) = \frac { f ( 16 ) - f ( 0 ) } { 16 - 0 }$.
A)
MVT applies; $- \frac { 16 \sqrt { 3 } } { 3 }$
B) MVT applies; 4
C) MVT applies; $\frac { 16 \sqrt { 3 } } { 3 }$
D) MVT applies; 8
E) MVT does not apply

Determine Whether the Mean Value Theorem Can Be Applied to the Function