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 .

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.

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

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.

Apply the product rule to .

Raise to the power of .

Raise to the power of .

Apply the product rule to .

Raise to the power of .

Raise to the power of .

Multiply .

Combine and .

Multiply by .

Move the negative in front of the fraction.

To write as a fraction with a common denominator, multiply by .

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Multiply and .

Multiply by .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Subtract from .

Move the negative in front of the fraction.

The final answer is .

The horizontal tangent lines on function are .

Find the Horizontal Tangent Line f(x)=x^3-7x^2