Question

How do you find the average rate of change for the function `y = 3x^2 -2x +1` on the indicated intervals [-1,1]?

Answer 1

The average rate of change of `y` with respect to `x` is `(Deltay)/(Deltax)`

Explanation:

`x_1 = -1` so `y_1 = 3(-1)^2-2(-1)+1 = 6`

`x_2 = 1` so `y_2 = 3(1)^2-2(1)+1 = 2`

The average rate of change is

`(Deltay)/(Deltax) = (y_2-y_1)/(x_2-x_1) = (6-2)/(1-(-1)) = 4/2=2`

The average rate of change is `2` (`y`'s per `x`).