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

question 15

Multiple Choice

$\text { Apply the Extended Mean Value Theorem to the functions } f ( x ) = \frac { 4 } { x } \text { and }$ $g ( x ) = x ^ { 2 } - 64$ 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) \(8 \sqrt { 3 }\)

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