Precalculus Examples

Find the Average Rate of Change f(x) = square root of 2x-5 from x_1=3 to x_2=5
from to
Step 1
Substitute using the average rate of change formula.
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Step 1.1
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 1.2
Substitute the equation for and , replacing in the function with the corresponding value.
Step 2
Simplify the expression.
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Step 2.1
Simplify the numerator.
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Step 2.1.1
Multiply by .
Step 2.1.2
Subtract from .
Step 2.1.3
Multiply by .
Step 2.1.4
Subtract from .
Step 2.1.5
Any root of is .
Step 2.1.6
Multiply by .
Step 2.2
Simplify the denominator.
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Step 2.2.1
Multiply by .
Step 2.2.2
Subtract from .
Step 3
The result can be shown in multiple forms.
Exact Form:
Decimal Form: