$\text { Evaluate the derivative of the function } f ( t ) = \frac { 8 t ^ { 2 } + 2 } { 5 t - 1 } \text { at the point } \left( 4 , \frac { 130 } { 19 } \right) \text {. }$
A) $f ^ { t } ( t ) = \frac { 566 } { 6859 }$
B) $f ^ { t } ( t ) = - \frac { 566 } { 361 }$
C) $f ^ { \t } ( t ) = \frac { 566 } { 19 }$
D) $f ^ { t } ( t ) = - \frac { 566 } { 19 }$
E) $f ^ { t } ( t ) = \frac { 566 } { 361 }$

Question

$\text { Evaluate the derivative of the function } f ( t ) = \frac { 8 t ^ { 2 } + 2 } { 5 t - 1 } \text { at the point } \left( 4 , \frac { 130 } { 19 } \right) \text {. }$ 
A) $f ^ { t } ( t ) = \frac { 566 } { 6859 }$
B) $f ^ { t } ( t ) = - \frac { 566 } { 361 }$
C) $f ^ { \t } ( t ) = \frac { 566 } { 19 }$
D) $f ^ { t } ( t ) = - \frac { 566 } { 19 }$
E) $f ^ { t } ( t ) = \frac { 566 } { 361 }$

Quizplus · Accepted Answer

To find the derivative of $f(t) = \frac{8t^2 + 2}{5t - 1}$, we use the quotient rule: $\left(\frac{u}{v}\right)' = \frac{u'v - uv'}{v^2}$, where $u = 8t^2 + 2$ and $v = 5t - 1$. After differentiation and simplification, evaluating at $t = 4$ gives the derivative as $\frac{566}{361}$.

A) ft(t)=5666859f ^ { t } ( t ) = \frac { 566 } { 6859 }ft(t)=6859566​

A) $f ^ { t } ( t ) = \frac { 566 } { 6859 }$