Finite Math Examples

Find the Average Rate of Change f(x)=4x-1/2 , (1,3)
,
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
Move the leading negative in into the numerator.
Step 3.3.2
Cancel the common factor.
Step 3.3.3
Rewrite the expression.
Step 3.4
Simplify the numerator.
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Step 3.4.1
Multiply .
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Step 3.4.1.1
Multiply by .
Step 3.4.1.2
Multiply by .
Step 3.4.2
Multiply by .
Step 3.4.3
To write as a fraction with a common denominator, multiply by .
Step 3.4.4
Combine and .
Step 3.4.5
Combine the numerators over the common denominator.
Step 3.4.6
Simplify the numerator.
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Step 3.4.6.1
Multiply by .
Step 3.4.6.2
Subtract from .
Step 3.4.7
Cancel the common factor of .
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Step 3.4.7.1
Move the leading negative in into the numerator.
Step 3.4.7.2
Cancel the common factor.
Step 3.4.7.3
Rewrite the expression.
Step 3.4.8
Subtract from .
Step 3.4.9
Subtract from .
Step 3.5
Simplify the denominator.
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Step 3.5.1
Multiply by .
Step 3.5.2
Multiply .
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Step 3.5.2.1
Multiply by .
Step 3.5.2.2
Multiply by .
Step 3.5.3
Subtract from .
Step 3.6
Divide by .