What is the rate of change of $f ( t ) = \frac { 8 t - 3 } { t + 6 }$ with respect to t when t = 45?
A) $\frac { 1 } { 51 }$
B) $- \frac { 1 } { 51 }$
C) 51
D) -51

Question

Quizplus · Accepted Answer

The rate of change of a function with respect to a variable is given by its derivative. For $f(t) = \frac{8t - 3}{t + 6}$, we find the derivative $f'(t)$ using the quotient rule: $$f'(t) = \frac{(8)(t + 6) - (8t - 3)(1)}{(t + 6)^2} = \frac{48 + 3}{(t + 6)^2} = \frac{51}{(t + 6)^2}.$$ Substituting $t = 45$, we get $f'(45) = \frac{51}{(45 + 6)^2} = \frac{51}{51^2} = \frac{1}{51}.$

What Is the Rate of Change Of f(t)=8t−3t+6f ( t ) = \frac { 8 t - 3 } { t + 6 }f(t)=t+68t−3​

What Is the Rate of Change Of $f ( t ) = \frac { 8 t - 3 } { t + 6 }$