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Precalculus Examples
on ,
Step 1
Write as an equation.
Step 2
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
Step 3.1
Simplify the numerator.
Step 3.1.1
Multiply by by adding the exponents.
Step 3.1.1.1
Multiply by .
Step 3.1.1.1.1
Raise to the power of .
Step 3.1.1.1.2
Use the power rule to combine exponents.
Step 3.1.1.2
Add and .
Step 3.1.2
Raise to the power of .
Step 3.1.3
Simplify each term.
Step 3.1.3.1
Raise to the power of .
Step 3.1.3.2
Multiply by .
Step 3.1.4
Subtract from .
Step 3.1.5
Multiply by .
Step 3.1.6
Subtract from .
Step 3.1.7
Add and .
Step 3.2
Simplify the denominator.
Step 3.2.1
Multiply by .
Step 3.2.2
Add and .
Step 3.3
Divide by .