# What is the average rate of change for the function over the interval, f(x)= 3/(x-2) between x =4 and x=7?

Mar 21, 2018

The average rate of change is $= - \frac{3}{10}$

#### Explanation:

The average rate of change of a function $f \left(x\right)$ over the interval $\left[a , b\right]$ is

$= \frac{f \left(b\right) - f \left(a\right)}{b - a}$

Here,

$f \left(x\right) = \frac{3}{x - 2}$

and $\left[a , b\right] = \left[4 , 7\right]$

$f \left(b\right) = f \left(7\right) = \frac{3}{7 - 2} = \frac{3}{5}$

$f \left(a\right) = f \left(4\right) = \frac{3}{4 - 2} = \frac{3}{2}$

Therefore,

The rate of change is

$= \frac{f \left(b\right) - f \left(a\right)}{b - a}$

$= \frac{\frac{3}{5} - \frac{3}{2}}{7 - 4}$

$= - \frac{9}{10} \cdot \frac{1}{3} = - \frac{3}{10}$

Mar 21, 2018

The average rate of change is $- \frac{3}{10}$

#### Explanation:

Average rate of change is given by

$A = \frac{f \left(b\right) - f \left(a\right)}{b - a}$

So the average rate of change here will be

$A = \frac{f \left(7\right) - f \left(4\right)}{7 - 4}$

$A = \frac{\frac{3}{5} - \frac{3}{2}}{3}$

$A = \frac{- \frac{9}{10}}{3}$

$A = - \frac{3}{10}$

Hopefully this helps!