Precalculus Examples

Find the Average Rate of Change f(x) = square root of x^3-4 , 2<=x<=5
,
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
Subtract from .
Step 3.1.3
Rewrite as .
Step 3.1.4
Pull terms out from under the radical, assuming positive real numbers.
Step 3.1.5
Raise to the power of .
Step 3.1.6
Subtract from .
Step 3.1.7
Rewrite as .
Step 3.1.8
Pull terms out from under the radical, assuming positive real numbers.
Step 3.1.9
Multiply by .
Step 3.1.10
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 .