# 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 $$4$$$.

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