# Calculus Examples

By the Sum Rule, the derivative of with respect to is .

Differentiate using the Power Rule which states that is where .

Since is constant with respect to , the derivative of with respect to is .

Add and .

Set the derivative equal to .

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 .

Take the cube root of both sides of the equation to eliminate the exponent on the left side.

Simplify .

Rewrite as .

Pull terms out from under the radical, assuming positive real numbers.

Substitute the values of which cause the derivative to be into the original function.

Raising to any positive power yields .

Subtract from .

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

Set-Builder Notation:

Since there are no values of where the derivative is undefined, there are no additional critical points.