What is the rate of change of $f ( t ) = \frac { 7 t - 4 } { t + 3 }$ with respect to t when t = 3?
A) $\frac { 25 } { 36 }$
B) $\frac { 19 } { 6 }$
C) 6
D) $\frac { 5 } { 3 }$

Question

Quizplus · Accepted Answer

The rate of change of a function with respect to a variable is given by its derivative. To find the derivative of $f(t) = \frac{7t - 4}{t + 3}$, we can use the quotient rule, which states that if $f(t) = \frac{g(t)}{h(t)}$, then $f'(t) = \frac{g'(t)h(t) - g(t)h'(t)}{[h(t)]^2}$. Applying this to our function, we get $f'(t) = \frac{(7)(t + 3) - (7t - 4)(1)}{(t + 3)^2} = \frac{21 + 7t - 7t + 4}{(t + 3)^2} = \frac{25}{(t + 3)^2}$. Evaluating this derivative at $t = 3$ gives $f'(3) = \frac{25}{(3 + 3)^2} = \frac{25}{36}$.

What Is the Rate of Change Of f(t)=7t−4t+3f ( t ) = \frac { 7 t - 4 } { t + 3 }f(t)=t+37t−4​

What Is the Rate of Change Of $f ( t ) = \frac { 7 t - 4 } { t + 3 }$