# How do I find the average rate of change of a function like f(x) = 4x?

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5
Sep 25, 2014

Usually we would need an interval to find the average rate of change. This is a linear function with a constant rate of change or slope so the slope and the average rate of change are the same value. Because of this reason a linear function does not need an interval.

This function is in slope intercept form, $y = m x + b$, where $m$ is the slope.

$y = 4 x$

We see that the slope is $4$.

Just for example sake lets find the average rate of change with an interval of $x = 2$ to $x = 5$.

Average rate of change$= \frac{f \left(b\right) - f \left(a\right)}{b - a}$

In this example:

$f \left(x\right) = 4 x$
$a = 2$
$b = 5$

Average rate of change$= \frac{f \left(5\right) - f \left(2\right)}{5 - 2}$

$= \frac{4 \left(5\right) - 4 \left(2\right)}{5 - 2}$

$= \frac{20 - 8}{3}$

$= \frac{12}{3}$

$= 4$

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