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

1 Answer
AJ Speller
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=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

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