Precalculus Examples

Find the Average Rate of Change f(x)=x^3+x
Step 1
Consider the difference quotient formula.
Step 2
Find the components of the definition.
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Step 2.1
Evaluate the function at .
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Step 2.1.1
Replace the variable with in the expression.
Step 2.1.2
Simplify the result.
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Step 2.1.2.1
Remove parentheses.
Step 2.1.2.2
Use the Binomial Theorem.
Step 2.1.2.3
The final answer is .
Step 2.2
Reorder.
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Step 2.2.1
Move .
Step 2.2.2
Move .
Step 2.2.3
Move .
Step 2.2.4
Move .
Step 2.2.5
Move .
Step 2.2.6
Reorder and .
Step 2.3
Find the components of the definition.
Step 3
Plug in the components.
Step 4
Simplify.
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Step 4.1
Simplify the numerator.
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Step 4.1.1
Apply the distributive property.
Step 4.1.2
Subtract from .
Step 4.1.3
Add and .
Step 4.1.4
Subtract from .
Step 4.1.5
Add and .
Step 4.1.6
Factor out of .
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Step 4.1.6.1
Factor out of .
Step 4.1.6.2
Factor out of .
Step 4.1.6.3
Factor out of .
Step 4.1.6.4
Raise to the power of .
Step 4.1.6.5
Factor out of .
Step 4.1.6.6
Factor out of .
Step 4.1.6.7
Factor out of .
Step 4.1.6.8
Factor out of .
Step 4.2
Reduce the expression by cancelling the common factors.
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Step 4.2.1
Cancel the common factor of .
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Step 4.2.1.1
Cancel the common factor.
Step 4.2.1.2
Divide by .
Step 4.2.2
Simplify the expression.
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Step 4.2.2.1
Move .
Step 4.2.2.2
Move .
Step 4.2.2.3
Reorder and .
Step 5