Precalculus Examples

Find the Average Rate of Change g(x) = cube root of x+4 ; -5<=x<=0
;
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
Pull terms out from under the radical, assuming real numbers.
Step 3.1.3
Simplify each term.
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Step 3.1.3.1
Rewrite as .
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Step 3.1.3.1.1
Rewrite as .
Step 3.1.3.1.2
Rewrite as .
Step 3.1.3.2
Pull terms out from under the radical.
Step 3.1.3.3
Rewrite as .
Step 3.1.4
Apply the distributive property.
Step 3.1.5
Multiply .
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Step 3.1.5.1
Multiply by .
Step 3.1.5.2
Multiply by .
Step 3.1.6
Multiply by .
Step 3.1.7
Add and .
Step 3.1.8
Subtract from .
Step 3.1.9
Add and .
Step 3.2
Simplify the denominator.
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Step 3.2.1
Multiply by .
Step 3.2.2
Add and .
Step 4
The result can be shown in multiple forms.
Exact Form:
Decimal Form: