# Consider the function f(x) = (x)/(x+2) on the interval [1, 4], how do you find the average or mean slope of the function on this interval?

Sep 4, 2017

The mean slope is $= \frac{1}{9}$

#### Explanation:

The average or mean slope of the function $y = f \left(x\right)$ on an interval $\left[{x}_{1} , {x}_{2}\right]$ is

$\frac{\Delta y}{\Delta x} = \frac{f \left({x}_{2}\right) - f \left({x}_{1}\right)}{{x}_{2} - {x}_{1}}$

Here,

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

And the interval is $= \left[1 , 4\right]$

Therefore,

$f \left(1\right) = \frac{1}{1 + 2} = \frac{1}{3}$

$f \left(4\right) = \frac{4}{4 + 2} = \frac{4}{6} = \frac{2}{3}$

So,

$\frac{\Delta y}{\Delta x} = \frac{f \left(4\right) - f \left(1\right)}{4 - 1} = \frac{\frac{2}{3} - \frac{1}{3}}{4 - 1} = \frac{1}{3} \cdot \frac{1}{3} = \frac{1}{9}$