Find the average rate of change for the function between the given values.
-$f ( x ) = \frac { 3 } { x + 2 } ;$ from 1 to 4
A) $- 28$
B) $- 2$
C) $- \frac { 1 } { 6 }$
D) $\frac { 1 } { 2 }$

Question

Quizplus · Accepted Answer

The average rate of change of a function $f(x)$ between two points $x = a$ and $x = b$ is given by $\frac{f(b) - f(a)}{b - a}$. For $f(x) = \frac{3}{x + 2}$, from $x = 1$ to $x = 4$, we calculate $f(1) = \frac{3}{1 + 2} = 1$ and $f(4) = \frac{3}{4 + 2} = \frac{1}{2}$. Thus, the average rate of change is $\frac{\frac{1}{2} - 1}{4 - 1} = \frac{-\frac{1}{2}}{3} = -\frac{1}{6}$.

Find the Average Rate of Change for the Function Between f(x)=3x+2;f ( x ) = \frac { 3 } { x + 2 } ;f(x)=x+23​;

Find the Average Rate of Change for the Function Between $f ( x ) = \frac { 3 } { x + 2 } ;$