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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
Reorder terms.
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
Subtract from 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 2.4
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 2.5
Any root of is .
Step 2.6
The complete solution is the result of both the positive and negative portions of the solution.
Step 2.6.1
First, use the positive value of the to find the first solution.
Step 2.6.2
Next, use the negative value of the to find the second solution.
Step 2.6.3
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
Multiply by .
Step 4.1.2.1.2
One to any power is one.
Step 4.1.2.1.3
Multiply by .
Step 4.1.2.2
Subtract from .
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
Multiply by .
Step 4.2.2.1.2
Multiply by by adding the exponents.
Step 4.2.2.1.2.1
Multiply by .
Step 4.2.2.1.2.1.1
Raise to the power of .
Step 4.2.2.1.2.1.2
Use the power rule to combine exponents.
Step 4.2.2.1.2.2
Add and .
Step 4.2.2.1.3
Raise to the power of .
Step 4.2.2.2
Add and .
Step 4.3
List all of the points.
Step 5