Question

Question #9a072

Answer 1

The average rate of change of `f(x) = x^3 - x` over the interval `(1,5)` is 30.

Explanation:

The average rate of change of a function over an interval `(a,b)` is provided by `(f(b) - f(a))/(b-a)`

So if we plug in your function as `f(x)` on the interval (1,5) into the formula, `(f(5) - f(1))/(5-1)` which is equal to `(((5)^3-(5)) - ((1)^3-(1)))/4`.

If you simplify from here, you will get `(120-0)/4` which further simplifies to `30`.