Precalculus Examples

Find the Average Rate of Change f(x)=1/x on [1,3]
on
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
Cancel the common factor of .
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Step 3.1.1
Cancel the common factor.
Step 3.1.2
Rewrite the expression.
Step 3.2
Multiply the numerator and denominator of the fraction by .
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Step 3.2.1
Multiply by .
Step 3.2.2
Combine.
Step 3.3
Apply the distributive property.
Step 3.4
Cancel the common factor of .
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Step 3.4.1
Cancel the common factor.
Step 3.4.2
Rewrite the expression.
Step 3.5
Simplify the numerator.
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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
Simplify the denominator.
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Step 3.6.1
Multiply by .
Step 3.6.2
Multiply .
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Step 3.6.2.1
Multiply by .
Step 3.6.2.2
Multiply by .
Step 3.6.3
Subtract from .
Step 3.7
Reduce the expression by cancelling the common factors.
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Step 3.7.1
Cancel the common factor of and .
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Step 3.7.1.1
Factor out of .
Step 3.7.1.2
Cancel the common factors.
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Step 3.7.1.2.1
Factor out of .
Step 3.7.1.2.2
Cancel the common factor.
Step 3.7.1.2.3
Rewrite the expression.
Step 3.7.2
Move the negative in front of the fraction.