# Calculus Examples

Find the Absolute Max and Min over the Interval
,
Find the first derivative.
By the Sum Rule, the derivative of with respect to is .
Evaluate .
Since is constant with respect to , the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Multiply by .
Since is constant with respect to , the derivative of with respect to is .
Set the first derivative equal to zero.
Divide each term by and simplify.
Divide each term in by .
Reduce the expression by cancelling the common factors.
Cancel the common factor.
Divide by .
Divide by .
Use the endpoints and all critical points on the interval to test for any absolute extrema over the given interval.
Evaluate the function at .
Simplify each term.
Remove parentheses around .
One to any power is one.
Multiply by .
Subtract from .
Evaluate the function at .
Simplify each term.
Multiply by by adding the exponents.
Combine and
Raise to the power of .
Use the power rule to combine exponents.