What is the rate of change of $f ( t ) = \frac { 4 t - 5 } { t + 4 }$ with respect to t when t = 17?
A) 21
B) -21
C) $- \frac { 1 } { 21 }$
D) $\frac { 1 } { 21 }$

Question

Quizplus · Accepted Answer

The rate of change of a function with respect to a variable is given by its derivative. For $f(t) = \frac{4t - 5}{t + 4}$, we find the derivative $f'(t)$ using the quotient rule: $f'(t) = \frac{(t + 4)(4) - (4t - 5)(1)}{(t + 4)^2} = \frac{16 + 1}{(t + 4)^2} = \frac{17}{(t + 4)^2}$. Substituting $t = 17$, we get $f'(17) = \frac{17}{(17 + 4)^2} = \frac{17}{21^2} = \frac{1}{21}$.

What Is the Rate of Change Of f(t)=4t−5t+4f ( t ) = \frac { 4 t - 5 } { t + 4 }f(t)=t+44t−5​

What Is the Rate of Change Of $f ( t ) = \frac { 4 t - 5 } { t + 4 }$