Precalculus Examples

Find the Average Rate of Change f(x)=3x^2+3 on [3,5]
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
Simplify the numerator.
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Step 3.1.1
Raise to the power of .
Step 3.1.2
Multiply by .
Step 3.1.3
Simplify each term.
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Step 3.1.3.1
Multiply by by adding the exponents.
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Step 3.1.3.1.1
Multiply by .
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Step 3.1.3.1.1.1
Raise to the power of .
Step 3.1.3.1.1.2
Use the power rule to combine exponents.
Step 3.1.3.1.2
Add and .
Step 3.1.3.2
Raise to the power of .
Step 3.1.4
Add and .
Step 3.1.5
Multiply by .
Step 3.1.6
Add and .
Step 3.1.7
Subtract from .
Step 3.2
Simplify the denominator.
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Step 3.2.1
Multiply by .
Step 3.2.2
Subtract from .
Step 3.3
Divide by .