Question

How do you find the average rate of change of `f(x)=4x` over the interval [0, 9]?

Answer 1

`4`

Explanation:

The average rate of change of a function `f(x)` on the interval `[a,b]` is given by the slope of the seant line connecting `(a,f(a))` and `(b(f,b))`, or:

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

Here, where `f(x)=4x`, we see that we have a linear function, where the rate of change is always `4`, but we can still show that the average rate of change will be `4` using the formula:

`=(4(9)-4(0))/(9-0)=(4(9-0))/(9-0)=4`