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
Evaluate .
Step 1.1.4.1
Since is constant with respect to , the derivative of with respect to is .
Step 1.1.4.2
Differentiate using the Power Rule which states that is where .
Step 1.1.4.3
Multiply by .
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
Substitute into the equation. This will make the quadratic formula easy to use.
Step 2.3
Factor the left side of the equation.
Step 2.3.1
Factor out of .
Step 2.3.1.1
Factor out of .
Step 2.3.1.2
Factor out of .
Step 2.3.1.3
Factor out of .
Step 2.3.1.4
Factor out of .
Step 2.3.1.5
Factor out of .
Step 2.3.2
Factor using the perfect square rule.
Step 2.3.2.1
Rewrite as .
Step 2.3.2.2
Check that the middle term is two times the product of the numbers being squared in the first term and third term.
Step 2.3.2.3
Rewrite the polynomial.
Step 2.3.2.4
Factor using the perfect square trinomial rule , where and .
Step 2.4
Divide each term in by and simplify.
Step 2.4.1
Divide each term in by .
Step 2.4.2
Simplify the left side.
Step 2.4.2.1
Cancel the common factor of .
Step 2.4.2.1.1
Cancel the common factor.
Step 2.4.2.1.2
Divide by .
Step 2.4.3
Simplify the right side.
Step 2.4.3.1
Divide by .
Step 2.5
Set the equal to .
Step 2.6
Add to both sides of the equation.
Step 2.7
Substitute the real value of back into the solved equation.
Step 2.8
Solve the equation for .
Step 2.8.1
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 2.8.2
Any root of is .
Step 2.8.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 2.8.3.1
First, use the positive value of the to find the first solution.
Step 2.8.3.2
Next, use the negative value of the to find the second solution.
Step 2.8.3.3
The complete solution is the result of both the positive and negative portions of the solution.
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
One to any power is one.
Step 4.1.2.1.2
Multiply by .
Step 4.1.2.1.3
One to any power is one.
Step 4.1.2.1.4
Multiply by .
Step 4.1.2.1.5
Multiply by .
Step 4.1.2.2
Simplify by adding and subtracting.
Step 4.1.2.2.1
Subtract from .
Step 4.1.2.2.2
Add and .
Step 4.2
Evaluate at .
Step 4.2.1
Substitute for .
Step 4.2.2
Simplify.
Step 4.2.2.1
Simplify each term.
Step 4.2.2.1.1
Raise to the power of .
Step 4.2.2.1.2
Multiply by .
Step 4.2.2.1.3
Raise to the power of .
Step 4.2.2.1.4
Multiply by .
Step 4.2.2.1.5
Multiply by .
Step 4.2.2.2
Simplify by adding and subtracting.
Step 4.2.2.2.1
Add and .
Step 4.2.2.2.2
Subtract from .
Step 4.3
List all of the points.
Step 5