Calculus Examples

Set as a function of .
Differentiate using the Power Rule which states that is where .
Set the derivative equal to then solve the equation .
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Rewrite as a set of linear factors.
Divide each term by and simplify.
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Divide each term in by .
Simplify the left side of the equation by cancelling the common factors.
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Multiply by to get .
Reduce the expression by cancelling the common factors.
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Cancel the common factor.
Divide by to get .
Divide by to get .
Take the root of both sides of the equation to eliminate the exponent on the left side.
The complete solution is the result of both the positive and negative portions of the solution.
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Simplify the right side of the equation.
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Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
is equal to .
Solve the original function at .
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Replace the variable with in the expression.
Simplify the result.
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Remove parentheses around .
Raising to any positive power yields .
The final answer is .
The horizontal tangent lines on function are .
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