# 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.

Enter a function:

Enter an interval: [, ]

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## 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 $4$.