# Determine the average rate of change of the given function between x=-2 and x=3.

## Question:

Determine the average rate of change of the given function between x=-2 and x=3.

h(x) = x{eq}^2 {/eq} + 3x

## Average Rate of Change:

The average rate of change of the function {eq}f(x) {/eq} between {eq}x=a {/eq} and {eq}x=b {/eq} is defined by {eq}f_{avg} = \displaystyle \displaystyle \frac{f(b) - f(a)}{b-a} {/eq}.

It tells us the value of the change in {eq}y {/eq} over the change in {eq}x {/eq} or {eq}\displaystyle \displaystyle \frac{\Delta y}{\Delta x} {/eq}.

We will use this formula to find the average rate of change of the given function.

## Answer and Explanation: 1

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We find first the values of {eq}f(3) {/eq} and {eq}f(-2) {/eq} by plugging in {eq}x=3 {/eq} and {eq}x=-2 {/eq} into the given function:

{eq}\begi...

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Average Rate of Change: Definition, Formula & Examples

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Chapter 20 / Lesson 5
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Finding the average rate of change is similar to finding the slope of a line. Study the definition of average rate of change, its formula, and examples of this concept.