Precalculus Examples

Find the Average Rate of Change f(x)=10 cube root of x-5
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
The final answer is .
Step 2.2
Find the components of the definition.
Step 3
Plug in the components.
Step 4
Simplify the numerator.
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Step 4.1
Use to rewrite as .
Step 4.2
Use to rewrite as .
Step 4.3
Apply the distributive property.
Step 4.4
Multiply by .
Step 4.5
Multiply by .
Step 4.6
Add and .
Step 4.7
Add and .
Step 4.8
Factor out of .
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Step 4.8.1
Factor out of .
Step 4.8.2
Factor out of .
Step 4.8.3
Factor out of .
Step 5