Average rate of change - PracticeCalculus

Lesson · Average rate of change

Before we can talk about how fast something changes at an instant, we need the everyday idea of an average rate of change. It is the change in output divided by the change in input:

\frac{f(b) - f(a)}{b - a}

For $f(x) = x^2$ from $x = 1$ to $x = 3$ : $\dfrac{9 - 1}{3 - 1} = \dfrac{8}{2} = 4$ .

Find the average rate of change of $f(x) = x^2$ from $x = 1$ to $x = 3$ .

\frac{f(3) - f(1)}{3 - 1}