Precalculus Examples

Find the Average Rate of Change s(t) = square root of 2t , [2,8]
,
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
Multiply by .
Step 3.1.2
Rewrite as .
Step 3.1.3
Pull terms out from under the radical, assuming positive real numbers.
Step 3.1.4
Multiply by .
Step 3.1.5
Rewrite as .
Step 3.1.6
Pull terms out from under the radical, assuming positive real numbers.
Step 3.1.7
Multiply by .
Step 3.1.8
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
Cancel the common factor of and .
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Step 3.3.1
Factor out of .
Step 3.3.2
Cancel the common factors.
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Step 3.3.2.1
Factor out of .
Step 3.3.2.2
Cancel the common factor.
Step 3.3.2.3
Rewrite the expression.