Question

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

Answer 1

The average rate of change is `6` (`f` units per `x` unit)

Explanation:

The rate of change is the ratio of the change of one quantity divided by the change of another.

Average rate of change of a function `f(x)` (with respect to `x`) is the change in `f(x)` divided by the change in `x`, so

Average rate of change of a function `f(x)` on an interval `[a,b]` is:

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

In this question: the function is `f(x) = x^3+2x^2+x` and the interval is `[a,b] = [-1,2]`

So the average rate of change of `f` on the interval is:

`(f(2)-f(-1))/(2-(-1)) = (18-0)/(2+1) = 18/3 = 6`.

If we had units for `x` and `f(x)` we would use them as `f` units per `x` unit