$\text { Apply the Extended Mean Value Theorem to the functions } f ( x ) = \frac { 4 } { x } \text { and }$

$\text { Apply the Extended Mean Value Theorem to the functions } f ( x ) = \frac { 4 } { x } \text { and }$ $g ( x ) = x ^ { 2 } - 64$ on the interval $[ 4,8 ]$ , and find all values $c$ in the interval $( 4,8 )$ such that $\frac { f ^ { t } ( c ) } { g ^ {t } ( c ) } = \frac { f ( 8 ) - f ( 4 ) } { g ( 8 ) - g ( 4 ) }$

A) $4 \sqrt [ 3 ] { 2 }$
B) $2 \sqrt [ 3 ] { 12 }$
C) $2 \sqrt { 6 }$
D) $4 \sqrt [ 3 ] { 3 }$
E) $8 \sqrt { 3 }$