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Calculus Examples
Step 1
Step 1.1
Find the first derivative.
Step 1.1.1
Differentiate using the Product Rule which states that is where and .
Step 1.1.2
Differentiate.
Step 1.1.2.1
By the Sum Rule, the derivative of with respect to is .
Step 1.1.2.2
Differentiate using the Power Rule which states that is where .
Step 1.1.2.3
Since is constant with respect to , the derivative of with respect to is .
Step 1.1.2.4
Simplify the expression.
Step 1.1.2.4.1
Add and .
Step 1.1.2.4.2
Multiply by .
Step 1.1.2.5
Differentiate using the Power Rule which states that is where .
Step 1.1.2.6
Simplify by adding terms.
Step 1.1.2.6.1
Multiply by .
Step 1.1.2.6.2
Add and .
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
Add to both sides of the equation.
Step 2.3
Divide each term in by and simplify.
Step 2.3.1
Divide each term in by .
Step 2.3.2
Simplify the left side.
Step 2.3.2.1
Cancel the common factor of .
Step 2.3.2.1.1
Cancel the common factor.
Step 2.3.2.1.2
Divide by .
Step 2.3.3
Simplify the right side.
Step 2.3.3.1
Divide by .
Step 3
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
Step 4.1
Evaluate at .
Step 4.1.1
Substitute for .
Step 4.1.2
Simplify.
Step 4.1.2.1
Multiply by .
Step 4.1.2.2
Subtract from .
Step 4.2
List all of the points.
Step 5