# Average Rate of Change Calculator

The calculator will find the average rate of change of the given function on the given interval, with steps shown.

## Solution

**Your input: find the average rate of change of $$$f\left(x\right)=x^{2}$$$ on the interval $$$\left[1,3\right]$$$.**

The average rate of change of $$$f\left(x\right)$$$ on the interval $$$[a,b]$$$ is $$$\frac{f(b)-f(a)}{b-a}$$$.

We have that $$$a=1$$$, $$$b=3$$$, $$$f\left(x\right)=x^{2}$$$.

Thus, $$$\frac{f(b)-f(a)}{b-a}=\frac{\color{red}{\left(3\right)}^{2}-\left(\color{red}{1}^{2}\right)}{3-\left(1\right)}=4$$$.

**Answer: the average rate of change is $$$4$$$.**