Calculus Examples

Find Where dy/dx is Equal to Zero
Differentiate both sides of the equation.
The derivative of with respect to is .
Differentiate the right side of the equation.
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Differentiate.
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By the Sum Rule, the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Evaluate .
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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 .
Reform the equation by setting the left side equal to the right side.
Replace with .
Set then solve for in terms of .
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Factor the left side of the equation.
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Factor out of .
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Factor out of .
Factor out of .
Factor out of .
Rewrite as .
Factor.
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Since both terms are perfect squares, factor using the difference of squares formula, where and .
Remove unnecessary parentheses.
Divide each term by and simplify.
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Divide each term in by .
Reduce the expression by cancelling the common factors.
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Cancel the common factor.
Divide by .
Divide by .
Set equal to and solve for .
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Set the factor equal to .
Subtract from both sides of the equation.
Set equal to and solve for .
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Set the factor equal to .
Add to both sides of the equation.
The solution is the result of and .
Simplify .
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Simplify each term.
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Raising to any positive power yields .
Raising to any positive power yields .
Multiply by .
Add and .
Simplify .
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Simplify each term.
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Raise to the power of .
Raise to the power of .
Multiply by .
Subtract from .
Find the points where .
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