# How do you find the average rate of change for the function f(x) = x^3 − 3x^2 on the indicated intervals [0,10]?

Aug 9, 2015

Average rate of change is 70. To put more meaning into it, it is 70 units of a per unit of b. Example: 70 mph or 70 Kelvins per second.

#### Explanation:

Average rate of change is written as:
$\frac{\Delta f \left(x\right)}{\Delta x} = \frac{f \left({x}_{a}\right) - f \left({x}_{b}\right)}{{x}_{a} - {x}_{b}}$

Your given interval is $\left[0 , 10\right]$. So ${x}_{a} = 0$ and ${x}_{b} = 10$.

Plugging in the values should give 70.

This is an introduction to the derivative .