# Calculus Examples

Step 1
Find the first derivative.
Step 1.1
Find the first derivative.
Step 1.1.1
By the Sum Rule, the derivative of with respect to is .
Step 1.1.2
Differentiate using the Power Rule which states that is where .
Step 1.1.3
Since is constant with respect to , the derivative of with respect to is .
Step 1.1.4
Step 1.2
The first derivative of with respect to is .
Step 2
Set the first derivative equal to then solve the equation .
Step 2.1
Set the first derivative equal to .
Step 2.2
Divide each term in by and simplify.
Step 2.2.1
Divide each term in by .
Step 2.2.2
Simplify the left side.
Step 2.2.2.1
Cancel the common factor of .
Step 2.2.2.1.1
Cancel the common factor.
Step 2.2.2.1.2
Divide by .
Step 2.2.3
Simplify the right side.
Step 2.2.3.1
Divide by .
Step 2.3
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 2.4
Simplify .
Step 2.4.1
Rewrite as .
Step 2.4.2
Pull terms out from under the radical, assuming real numbers.
Step 3
Find the values where the derivative is undefined.
Step 3.1
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Step 4
Evaluate at each value where the derivative is or undefined.
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
Subtract from .
Step 4.2
List all of the points.
Step 5