Precalculus Examples

Find the Average Rate of Change f(x)=x^(3/2) on 1 , 4
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
Rewrite as .
Step 3.1.2
Apply the power rule and multiply exponents, .
Step 3.1.3
Cancel the common factor of .
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Step 3.1.3.1
Cancel the common factor.
Step 3.1.3.2
Rewrite the expression.
Step 3.1.4
Raise to the power of .
Step 3.1.5
One to any power is one.
Step 3.1.6
Multiply by .
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 .