The instantaneous rate of change of $f ( x ) = \frac { 8 } { x + 1 }$ at c = 3 is

A)-2
B)-1
C) $- \frac { 1 } { 2 }$
D) $\frac { 1 } { 2 }$
E)2

Question

The instantaneous rate of change of $f ( x ) = \frac { 8 } { x + 1 }$ at c = 3 is

A)-2
B)-1
C) $- \frac { 1 } { 2 }$
D) $\frac { 1 } { 2 }$
E)2

Quizplus · Accepted Answer

The instantaneous rate of change of a function at a point is given by its derivative evaluated at that point. For $f(x) = \frac{8}{x+1}$, the derivative $f'(x)$ can be found using the quotient rule or recognizing it as a constant times the derivative of $1/(x+1)$. The derivative is $f'(x) = -\frac{8}{(x+1)^2}$. Evaluating this at $c = 3$ gives $f'(3) = -\frac{8}{(3+1)^2} = -\frac{8}{16} = -\frac{1}{2}$.

The Instantaneous Rate of Change Of f(x)=8x+1f ( x ) = \frac { 8 } { x + 1 }f(x)=x+18​

The Instantaneous Rate of Change Of $f ( x ) = \frac { 8 } { x + 1 }$