Calculus Examples

Step 1
Set as a function of .
Step 2
Find the derivative.
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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 .
Differentiate using the Constant Rule.
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Since is constant with respect to , the derivative of with respect to is .
Add and .
Step 3
Set the derivative equal to then solve the equation .
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Subtract from both sides of the equation.
Divide each term in by and simplify.
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Divide each term in by .
Simplify the left side.
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Cancel the common factor of .
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Cancel the common factor.
Divide by .
Simplify the right side.
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Divide by .
Step 4
Solve the original function at .
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Replace the variable with in the expression.
Simplify the result.
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Simplify each term.
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Raise to the power of .
Multiply by .
Simplify by subtracting numbers.
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Subtract from .
Subtract from .
The final answer is .
Step 5
The horizontal tangent line on function is .
Step 6
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