Set as a function of .

Differentiate.

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

Differentiate using the Power Rule which states that is where .

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 .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Divide each term by and simplify.

Divide each term in by .

Simplify .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Apply the distributive property.

Simplify the expression.

Multiply by .

Move to the left of .

Divide by .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .

Set the first factor equal to .

Set the next factor equal to and solve.

Set the next factor equal to .

Add to both sides of the equation.

The final solution is all the values that make true.

Replace the variable with in the expression.

Simplify the result.

Simplify each term.

Raising to any positive power yields .

Raising to any positive power yields .

Multiply by .

Add and .

The final answer is .

Replace the variable with in the expression.

Simplify the result.

Simplify each term.

Raise to the power of .

Raise to the power of .

Multiply by .

Subtract from .

The final answer is .

The horizontal tangent lines on function are .

Find the Horizontal Tangent Line y=x^3-3x^2