Find the average rate of change of $f(x)=x^2$ between $-2$ and $2$. Find the instantaneous rate of change at both of those points.

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Lesson Parent: 
Differentiation V: Derivatives and Rates of Change
Problem: 

Find the average rate of change of $f(x)=x^2$ between $-2$ and $2$. Find the instantaneous rate of change at both of those points.

Answer: 

SAMPLE SOLUTION

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Solution: 

From this lesson we know that the average rate of change is

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and that the instantaneous rate of change is $f'(x)$.

Therefore the average rate of change between $-2$ and $2$ is

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Now we know that $f(x)$ is a polynomial function and that the derivative of a polynomial is known. Therefore,

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So the instantaneous rate of change at $-2$ is <Sign in to see all the formulas> and the instantaneous rate of change at $2$ is <Sign in to see all the formulas>.