The instantaneous rate of change of $f ( x ) = \frac { 3 } { x + 1 }$ at c = 2 is

A) -3

B)
$- \frac { 1 } { 3 }$
C)
$\frac { 1 } { 3 }$
D) 1

E) 3

Question

The instantaneous rate of change of $f ( x ) = \frac { 3 } { x + 1 }$ at c = 2 is

A) -3
 
B)
 $- \frac { 1 } { 3 }$ 
C)
 $\frac { 1 } { 3 }$ 
D) 1

E) 3

Quizplus · Accepted Answer

The instantaneous rate of change of a function at a point is given by its derivative evaluated at that point. For $f(x) = \frac{3}{x + 1}$, 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 $f'(x) = -\frac{3}{(x + 1)^2}$. Evaluating this at $c = 2$ gives $f'(2) = -\frac{3}{(2 + 1)^2} = -\frac{3}{9} = -\frac{1}{3}$.

The Instantaneous Rate of Change Of f(x)=3x+1f ( x ) = \frac { 3 } { x + 1 }f(x)=x+13​

The Instantaneous Rate of Change Of $f ( x ) = \frac { 3 } { x + 1 }$