Question

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

Answer 1

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=mx+b`, where `m` is the slope.

`y=4x`

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`=(f(b)-f(a))/(b-a)`

In this example:

`f(x)=4x`
`a=2`
`b=5`

Average rate of change`=(f(5)-f(2))/(5-2)`

`=(4(5)-4(2))/(5-2)`

`=(20-8)/(3)`

`=12/3`

`=4`