Calculus Examples

Find the Horizontal Tangent Line f(x)=x^3
Step 1
Differentiate using the Power Rule which states that is where .
Step 2
Set the derivative equal to then solve the equation .
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Step 2.1
Divide each term in by and simplify.
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Step 2.1.1
Divide each term in by .
Step 2.1.2
Simplify the left side.
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Step 2.1.2.1
Cancel the common factor of .
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Step 2.1.2.1.1
Cancel the common factor.
Step 2.1.2.1.2
Divide by .
Step 2.1.3
Simplify the right side.
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Step 2.1.3.1
Divide by .
Step 2.2
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 2.3
Simplify .
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Step 2.3.1
Rewrite as .
Step 2.3.2
Pull terms out from under the radical, assuming positive real numbers.
Step 2.3.3
Plus or minus is .
Step 3
Solve the original function at .
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Step 3.1
Replace the variable with in the expression.
Step 3.2
Simplify the result.
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Step 3.2.1
Raising to any positive power yields .
Step 3.2.2
The final answer is .
Step 4
The horizontal tangent line on function is .
Step 5