Enter a problem...
Calculus Examples
Step 1
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
Evaluate .
Step 1.1.2.1
Since is constant with respect to , 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
Multiply by .
Step 1.1.3
Evaluate .
Step 1.1.3.1
Since is constant with respect to , the derivative of with respect to is .
Step 1.1.3.2
Differentiate using the Power Rule which states that is where .
Step 1.1.3.3
Multiply by .
Step 1.1.4
Differentiate using the Constant Rule.
Step 1.1.4.1
Since is constant with respect to , the derivative of with respect to is .
Step 1.1.4.2
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
Cancel the common factor of and .
Step 2.3.3.1.1
Factor out of .
Step 2.3.3.1.2
Cancel the common factors.
Step 2.3.3.1.2.1
Factor out of .
Step 2.3.3.1.2.2
Cancel the common factor.
Step 2.3.3.1.2.3
Rewrite the expression.
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
Simplify each term.
Step 4.1.2.1.1
Apply the product rule to .
Step 4.1.2.1.2
Raise to the power of .
Step 4.1.2.1.3
Raise to the power of .
Step 4.1.2.1.4
Cancel the common factor of .
Step 4.1.2.1.4.1
Factor out of .
Step 4.1.2.1.4.2
Factor out of .
Step 4.1.2.1.4.3
Cancel the common factor.
Step 4.1.2.1.4.4
Rewrite the expression.
Step 4.1.2.1.5
Combine and .
Step 4.1.2.1.6
Multiply by .
Step 4.1.2.1.7
Multiply .
Step 4.1.2.1.7.1
Combine and .
Step 4.1.2.1.7.2
Multiply by .
Step 4.1.2.1.8
Move the negative in front of the fraction.
Step 4.1.2.2
Combine fractions.
Step 4.1.2.2.1
Combine the numerators over the common denominator.
Step 4.1.2.2.2
Simplify the expression.
Step 4.1.2.2.2.1
Subtract from .
Step 4.1.2.2.2.2
Move the negative in front of the fraction.
Step 4.1.2.3
To write as a fraction with a common denominator, multiply by .
Step 4.1.2.4
Combine and .
Step 4.1.2.5
Combine the numerators over the common denominator.
Step 4.1.2.6
Simplify the numerator.
Step 4.1.2.6.1
Multiply by .
Step 4.1.2.6.2
Subtract from .
Step 4.1.2.7
Move the negative in front of the fraction.
Step 4.2
List all of the points.
Step 5