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Calculus Examples
Step 1
Step 1.1
Find the first derivative.
Step 1.1.1
Differentiate using the Quotient Rule which states that is where and .
Step 1.1.2
Differentiate.
Step 1.1.2.1
Differentiate using the Power Rule which states that is where .
Step 1.1.2.2
Move to the left of .
Step 1.1.2.3
By the Sum Rule, the derivative of with respect to is .
Step 1.1.2.4
Differentiate using the Power Rule which states that is where .
Step 1.1.2.5
Since is constant with respect to , the derivative of with respect to is .
Step 1.1.2.6
Simplify the expression.
Step 1.1.2.6.1
Add and .
Step 1.1.2.6.2
Multiply by .
Step 1.1.3
Simplify.
Step 1.1.3.1
Apply the distributive property.
Step 1.1.3.2
Apply the distributive property.
Step 1.1.3.3
Simplify the numerator.
Step 1.1.3.3.1
Simplify each term.
Step 1.1.3.3.1.1
Multiply by by adding the exponents.
Step 1.1.3.3.1.1.1
Move .
Step 1.1.3.3.1.1.2
Multiply by .
Step 1.1.3.3.1.2
Multiply by .
Step 1.1.3.3.2
Subtract from .
Step 1.1.3.4
Factor out of .
Step 1.1.3.4.1
Factor out of .
Step 1.1.3.4.2
Factor out of .
Step 1.1.3.4.3
Factor out of .
Step 1.2
The first derivative of with respect to is .
Step 2
Step 2.1
Set the first derivative equal to .
Step 2.2
Set the numerator equal to zero.
Step 2.3
Solve the equation for .
Step 2.3.1
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 2.3.2
Set equal to .
Step 2.3.3
Set equal to and solve for .
Step 2.3.3.1
Set equal to .
Step 2.3.3.2
Subtract from both sides of the equation.
Step 2.3.4
The final solution is all the values that make true.
Step 3
Step 3.1
Set the denominator in equal to to find where the expression is undefined.
Step 3.2
Solve for .
Step 3.2.1
Set the equal to .
Step 3.2.2
Subtract from both sides of the equation.
Step 4
Step 4.1
Evaluate at .
Step 4.1.1
Substitute for .
Step 4.1.2
Simplify.
Step 4.1.2.1
Raising to any positive power yields .
Step 4.1.2.2
Add and .
Step 4.1.2.3
Divide by .
Step 4.2
Evaluate at .
Step 4.2.1
Substitute for .
Step 4.2.2
Simplify.
Step 4.2.2.1
Raise to the power of .
Step 4.2.2.2
Add and .
Step 4.2.2.3
Divide by .
Step 4.3
Evaluate at .
Step 4.3.1
Substitute for .
Step 4.3.2
Simplify.
Step 4.3.2.1
Add and .
Step 4.3.2.2
The expression contains a division by . The expression is undefined.
Undefined
Undefined
Undefined
Step 4.4
List all of the points.
Step 5