# Consider the function  f(x)=1/sqrt(x+2) on the interval [-1, 23], how do you find the average or mean slope of the function on this interval?

May 12, 2017

The mean slope is $= - \frac{1}{30}$

#### Explanation:

The mean slope of a function $f \left(x\right)$ over an interval $\left[a , b\right]$ is

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

Here,

$f \left(x\right) = \frac{1}{\sqrt{x + 2}}$

$f \left(- 1\right) = \frac{1}{\sqrt{- 1 + 2}} = 1$

$f \left(23\right) = \frac{1}{\sqrt{23 + 2}} = \frac{1}{5}$

Therefore,

the mean slope is

$= \frac{f \left(23\right) - f \left(- 1\right)}{23 - \left(- 1\right)}$

$= \frac{\frac{1}{5} - 1}{24}$

$= - \frac{4}{5} \cdot \frac{1}{24} = - \frac{1}{30}$