Question

What is the average rate of change formula for a function?

Answer 1

For a function `f(x)` the average rate of change between `x=x_1` and `x=x_2` is
`color(white)("XXXX")` `(f(x_2)-f(x_1))/(x_2-x_1)`

Explanation:

(The above formula assumes that the function is continuous in the range `[x_1,x_2]`)

This is basically just a definition but you might think of "the average rate of change" as
`color(white)("XXXX")`the amount by which the function changes
`color(white)("XXXX")` `color(white)("XXXX")`divided by
`color(white)("XXXX")`the distance over which that change takes place