Calculus Examples

Set as a function of .
Find the derivative.
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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 .
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Divide each term by and simplify.
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Divide each term in by .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Divide by .
Take the root of both sides of the 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.
The absolute value is the distance between a number and zero. The distance between and is .
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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Raising to any positive power yields .
Multiply by .
The final answer is .
The horizontal tangent lines on function are .
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