Examples

Find the Average Rate of Change
, ,
Step 1
Write as a function.
Step 2
Substitute using the average rate of change formula.
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Step 2.1
The average rate of change of a function can be found by calculating the change in values of the two points divided by the change in values of the two points.
Step 2.2
Substitute the equation for and , replacing in the function with the corresponding value.
Step 3
Simplify the expression.
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Step 3.1
Simplify the numerator.
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Step 3.1.1
One to any power is one.
Step 3.1.2
Multiply by .
Step 3.1.3
Multiply by .
Step 3.1.4
Raising to any positive power yields .
Step 3.1.5
Multiply by .
Step 3.1.6
Add and .
Step 3.2
Simplify the denominator.
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Step 3.2.1
Multiply by .
Step 3.2.2
Add and .
Step 3.3
Divide by .
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