Finite Math Examples

Find the Average Rate of Change y=1/2x^2 , [1,2]
,
Step 1
Substitute using the average rate of change formula.
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Step 1.1
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 1.2
Substitute the equation for and , replacing in the function with the corresponding value.
Step 2
Simplify the expression.
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Step 2.1
Simplify the numerator.
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Step 2.1.1
Cancel the common factor of .
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Step 2.1.1.1
Factor out of .
Step 2.1.1.2
Cancel the common factor.
Step 2.1.1.3
Rewrite the expression.
Step 2.1.2
One to any power is one.
Step 2.1.3
Multiply by .
Step 2.1.4
To write as a fraction with a common denominator, multiply by .
Step 2.1.5
Combine and .
Step 2.1.6
Combine the numerators over the common denominator.
Step 2.1.7
Simplify the numerator.
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Step 2.1.7.1
Multiply by .
Step 2.1.7.2
Subtract from .
Step 2.2
Simplify the denominator.
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Step 2.2.1
Multiply by .
Step 2.2.2
Subtract from .
Step 2.3
Divide by .