Precalculus Examples

Find the Average Rate of Change f(x)=2x^2-2x-1 ; [1,3/2]
;
Step 1
Write as an equation.
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
Multiply the numerator and denominator of the fraction by .
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Step 3.1.1
Multiply by .
Step 3.1.2
Combine.
Step 3.2
Apply the distributive property.
Step 3.3
Cancel the common factor of .
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Step 3.3.1
Cancel the common factor.
Step 3.3.2
Rewrite the expression.
Step 3.4
Simplify the numerator.
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Step 3.4.1
Multiply by .
Step 3.4.2
Apply the product rule to .
Step 3.4.3
Raise to the power of .
Step 3.4.4
Raise to the power of .
Step 3.4.5
Cancel the common factor of .
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Step 3.4.5.1
Cancel the common factor.
Step 3.4.5.2
Rewrite the expression.
Step 3.4.6
Cancel the common factor of .
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Step 3.4.6.1
Factor out of .
Step 3.4.6.2
Cancel the common factor.
Step 3.4.6.3
Rewrite the expression.
Step 3.4.7
Multiply by .
Step 3.4.8
Multiply by .
Step 3.4.9
Multiply by .
Step 3.4.10
Simplify each term.
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Step 3.4.10.1
One to any power is one.
Step 3.4.10.2
Multiply by .
Step 3.4.10.3
Multiply by .
Step 3.4.11
Subtract from .
Step 3.4.12
Subtract from .
Step 3.4.13
Multiply .
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Step 3.4.13.1
Multiply by .
Step 3.4.13.2
Multiply by .
Step 3.4.14
Subtract from .
Step 3.4.15
Subtract from .
Step 3.4.16
Add and .
Step 3.5
Simplify the denominator.
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Step 3.5.1
Multiply .
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Step 3.5.1.1
Multiply by .
Step 3.5.1.2
Multiply by .
Step 3.5.2
Subtract from .
Step 3.6
Divide by .