# Find the Horizontal Tangent Line y=x^3-3x^2 Set as a function of .
Find the derivative.
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 .
Set the derivative equal to then solve the equation .
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.
Solve the original function at .
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 .
The final answer is .
Solve the original function at .
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 .
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