# Calculus Examples

Step 1

Step 1.1

Differentiate.

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 1.2

Evaluate .

Step 1.2.1

Since is constant with respect to , the derivative of with respect to is .

Step 1.2.2

Differentiate using the Power Rule which states that is where .

Step 1.2.3

Multiply by .

Step 1.3

Evaluate .

Step 1.3.1

Since is constant with respect to , the derivative of with respect to is .

Step 1.3.2

Differentiate using the Power Rule which states that is where .

Step 1.3.3

Multiply by .

Step 2

Step 2.1

Factor out of .

Step 2.1.1

Factor out of .

Step 2.1.2

Factor out of .

Step 2.1.3

Factor out of .

Step 2.1.4

Factor out of .

Step 2.1.5

Factor out of .

Step 2.2

If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .

Step 2.3

Set equal to .

Step 2.4

Set equal to and solve for .

Step 2.4.1

Set equal to .

Step 2.4.2

Solve for .

Step 2.4.2.1

Use the quadratic formula to find the solutions.

Step 2.4.2.2

Substitute the values , , and into the quadratic formula and solve for .

Step 2.4.2.3

Simplify.

Step 2.4.2.3.1

Simplify the numerator.

Step 2.4.2.3.1.1

Raise to the power of .

Step 2.4.2.3.1.2

Multiply .

Step 2.4.2.3.1.2.1

Multiply by .

Step 2.4.2.3.1.2.2

Multiply by .

Step 2.4.2.3.1.3

Add and .

Step 2.4.2.3.2

Multiply by .

Step 2.4.2.4

Simplify the expression to solve for the portion of the .

Step 2.4.2.4.1

Simplify the numerator.

Step 2.4.2.4.1.1

Raise to the power of .

Step 2.4.2.4.1.2

Multiply .

Step 2.4.2.4.1.2.1

Multiply by .

Step 2.4.2.4.1.2.2

Multiply by .

Step 2.4.2.4.1.3

Add and .

Step 2.4.2.4.2

Multiply by .

Step 2.4.2.4.3

Change the to .

Step 2.4.2.5

Simplify the expression to solve for the portion of the .

Step 2.4.2.5.1

Simplify the numerator.

Step 2.4.2.5.1.1

Raise to the power of .

Step 2.4.2.5.1.2

Multiply .

Step 2.4.2.5.1.2.1

Multiply by .

Step 2.4.2.5.1.2.2

Multiply by .

Step 2.4.2.5.1.3

Add and .

Step 2.4.2.5.2

Multiply by .

Step 2.4.2.5.3

Change the to .

Step 2.4.2.6

The final answer is the combination of both solutions.

Step 2.5

The final solution is all the values that make true.

Step 3

Split into separate intervals around the values that make the first derivative or undefined.

Step 4

Step 4.1

Replace the variable with in the expression.

Step 4.2

Simplify the result.

Step 4.2.1

Simplify each term.

Step 4.2.1.1

Raise to the power of .

Step 4.2.1.2

Multiply by .

Step 4.2.1.3

Raise to the power of .

Step 4.2.1.4

Multiply by .

Step 4.2.1.5

Multiply by .

Step 4.2.2

Simplify by adding and subtracting.

Step 4.2.2.1

Subtract from .

Step 4.2.2.2

Add and .

Step 4.2.3

The final answer is .

Step 5

Step 5.1

Replace the variable with in the expression.

Step 5.2

Simplify the result.

Step 5.2.1

Simplify each term.

Step 5.2.1.1

Raise to the power of .

Step 5.2.1.2

Multiply by .

Step 5.2.1.3

Raise to the power of .

Step 5.2.1.4

Multiply by .

Step 5.2.1.5

Multiply by .

Step 5.2.2

Simplify by adding and subtracting.

Step 5.2.2.1

Subtract from .

Step 5.2.2.2

Add and .

Step 5.2.3

The final answer is .

Step 6

Step 6.1

Replace the variable with in the expression.

Step 6.2

Simplify the result.

Step 6.2.1

Simplify each term.

Step 6.2.1.1

One to any power is one.

Step 6.2.1.2

Multiply by .

Step 6.2.1.3

One to any power is one.

Step 6.2.1.4

Multiply by .

Step 6.2.1.5

Multiply by .

Step 6.2.2

Simplify by subtracting numbers.

Step 6.2.2.1

Subtract from .

Step 6.2.2.2

Subtract from .

Step 6.2.3

The final answer is .

Step 7

Step 7.1

Replace the variable with in the expression.

Step 7.2

Simplify the result.

Step 7.2.1

Simplify each term.

Step 7.2.1.1

Raise to the power of .

Step 7.2.1.2

Multiply by .

Step 7.2.1.3

Raise to the power of .

Step 7.2.1.4

Multiply by .

Step 7.2.1.5

Multiply by .

Step 7.2.2

Simplify by subtracting numbers.

Step 7.2.2.1

Subtract from .

Step 7.2.2.2

Subtract from .

Step 7.2.3

The final answer is .

Step 8

Since the first derivative changed signs from negative to positive around , then there is a turning point at .

Step 9

Step 9.1

Find to find the y-coordinate of .

Step 9.1.1

Replace the variable with in the expression.

Step 9.1.2

Simplify .

Step 9.1.2.1

Remove parentheses.

Step 9.1.2.2

Simplify each term.

Step 9.1.2.2.1

Apply the product rule to .

Step 9.1.2.2.2

Raise to the power of .

Step 9.1.2.2.3

Use the Binomial Theorem.

Step 9.1.2.2.4

Simplify each term.

Step 9.1.2.2.4.1

Raise to the power of .

Step 9.1.2.2.4.2

Raise to the power of .

Step 9.1.2.2.4.3

Multiply by .

Step 9.1.2.2.4.4

Multiply by .

Step 9.1.2.2.4.5

Raise to the power of .

Step 9.1.2.2.4.6

Multiply by .

Step 9.1.2.2.4.7

Apply the product rule to .

Step 9.1.2.2.4.8

Raise to the power of .

Step 9.1.2.2.4.9

Multiply by .

Step 9.1.2.2.4.10

Rewrite as .

Step 9.1.2.2.4.10.1

Use to rewrite as .

Step 9.1.2.2.4.10.2

Apply the power rule and multiply exponents, .

Step 9.1.2.2.4.10.3

Combine and .

Step 9.1.2.2.4.10.4

Cancel the common factor of .

Step 9.1.2.2.4.10.4.1

Cancel the common factor.

Step 9.1.2.2.4.10.4.2

Rewrite the expression.

Step 9.1.2.2.4.10.5

Evaluate the exponent.

Step 9.1.2.2.4.11

Multiply by .

Step 9.1.2.2.4.12

Multiply by .

Step 9.1.2.2.4.13

Apply the product rule to .

Step 9.1.2.2.4.14

Raise to the power of .

Step 9.1.2.2.4.15

Rewrite as .

Step 9.1.2.2.4.16

Raise to the power of .

Step 9.1.2.2.4.17

Rewrite as .

Step 9.1.2.2.4.17.1

Factor out of .

Step 9.1.2.2.4.17.2

Rewrite as .

Step 9.1.2.2.4.18

Pull terms out from under the radical.

Step 9.1.2.2.4.19

Multiply by .

Step 9.1.2.2.4.20

Multiply by .

Step 9.1.2.2.4.21

Apply the product rule to .

Step 9.1.2.2.4.22

Raise to the power of .

Step 9.1.2.2.4.23

Multiply by .

Step 9.1.2.2.4.24

Rewrite as .

Step 9.1.2.2.4.24.1

Use to rewrite as .

Step 9.1.2.2.4.24.2

Apply the power rule and multiply exponents, .

Step 9.1.2.2.4.24.3

Combine and .

Step 9.1.2.2.4.24.4

Cancel the common factor of and .

Step 9.1.2.2.4.24.4.1

Factor out of .

Step 9.1.2.2.4.24.4.2

Cancel the common factors.

Step 9.1.2.2.4.24.4.2.1

Factor out of .

Step 9.1.2.2.4.24.4.2.2

Cancel the common factor.

Step 9.1.2.2.4.24.4.2.3

Rewrite the expression.

Step 9.1.2.2.4.24.4.2.4

Divide by .

Step 9.1.2.2.4.25

Raise to the power of .

Step 9.1.2.2.5

Add and .

Step 9.1.2.2.6

Add and .

Step 9.1.2.2.7

Subtract from .

Step 9.1.2.2.8

Cancel the common factor of and .

Step 9.1.2.2.8.1

Factor out of .

Step 9.1.2.2.8.2

Factor out of .

Step 9.1.2.2.8.3

Factor out of .

Step 9.1.2.2.8.4

Cancel the common factors.

Step 9.1.2.2.8.4.1

Factor out of .

Step 9.1.2.2.8.4.2

Cancel the common factor.

Step 9.1.2.2.8.4.3

Rewrite the expression.

Step 9.1.2.2.9

Apply the product rule to .

Step 9.1.2.2.10

Raise to the power of .

Step 9.1.2.2.11

Use the Binomial Theorem.

Step 9.1.2.2.12

Simplify each term.

Step 9.1.2.2.12.1

Raise to the power of .

Step 9.1.2.2.12.2

Multiply by by adding the exponents.

Step 9.1.2.2.12.2.1

Multiply by .

Step 9.1.2.2.12.2.1.1

Raise to the power of .

Step 9.1.2.2.12.2.1.2

Use the power rule to combine exponents.

Step 9.1.2.2.12.2.2

Add and .

Step 9.1.2.2.12.3

Raise to the power of .

Step 9.1.2.2.12.4

Multiply by .

Step 9.1.2.2.12.5

Multiply by .

Step 9.1.2.2.12.6

Apply the product rule to .

Step 9.1.2.2.12.7

Raise to the power of .

Step 9.1.2.2.12.8

Multiply by .

Step 9.1.2.2.12.9

Rewrite as .

Step 9.1.2.2.12.9.1

Use to rewrite as .

Step 9.1.2.2.12.9.2

Apply the power rule and multiply exponents, .

Step 9.1.2.2.12.9.3

Combine and .

Step 9.1.2.2.12.9.4

Cancel the common factor of .

Step 9.1.2.2.12.9.4.1

Cancel the common factor.

Step 9.1.2.2.12.9.4.2

Rewrite the expression.

Step 9.1.2.2.12.9.5

Evaluate the exponent.

Step 9.1.2.2.12.10

Multiply by .

Step 9.1.2.2.12.11

Apply the product rule to .

Step 9.1.2.2.12.12

Raise to the power of .

Step 9.1.2.2.12.13

Rewrite as .

Step 9.1.2.2.12.14

Raise to the power of .

Step 9.1.2.2.12.15

Rewrite as .

Step 9.1.2.2.12.15.1

Factor out of .

Step 9.1.2.2.12.15.2

Rewrite as .

Step 9.1.2.2.12.16

Pull terms out from under the radical.

Step 9.1.2.2.12.17

Multiply by .

Step 9.1.2.2.13

Add and .

Step 9.1.2.2.14

Subtract from .

Step 9.1.2.2.15

Cancel the common factor of and .

Step 9.1.2.2.15.1

Factor out of .

Step 9.1.2.2.15.2

Factor out of .

Step 9.1.2.2.15.3

Factor out of .

Step 9.1.2.2.15.4

Cancel the common factors.

Step 9.1.2.2.15.4.1

Factor out of .

Step 9.1.2.2.15.4.2

Cancel the common factor.

Step 9.1.2.2.15.4.3

Rewrite the expression.

Step 9.1.2.2.16

Apply the product rule to .

Step 9.1.2.2.17

Raise to the power of .

Step 9.1.2.2.18

Cancel the common factor of .

Step 9.1.2.2.18.1

Factor out of .

Step 9.1.2.2.18.2

Factor out of .

Step 9.1.2.2.18.3

Cancel the common factor.

Step 9.1.2.2.18.4

Rewrite the expression.

Step 9.1.2.2.19

Combine and .

Step 9.1.2.2.20

Rewrite as .

Step 9.1.2.2.21

Expand using the FOIL Method.

Step 9.1.2.2.21.1

Apply the distributive property.

Step 9.1.2.2.21.2

Apply the distributive property.

Step 9.1.2.2.21.3

Apply the distributive property.

Step 9.1.2.2.22

Simplify and combine like terms.

Step 9.1.2.2.22.1

Simplify each term.

Step 9.1.2.2.22.1.1

Multiply by .

Step 9.1.2.2.22.1.2

Multiply by .

Step 9.1.2.2.22.1.3

Multiply by .

Step 9.1.2.2.22.1.4

Multiply .

Step 9.1.2.2.22.1.4.1

Multiply by .

Step 9.1.2.2.22.1.4.2

Multiply by .

Step 9.1.2.2.22.1.4.3

Raise to the power of .

Step 9.1.2.2.22.1.4.4

Raise to the power of .

Step 9.1.2.2.22.1.4.5

Use the power rule to combine exponents.

Step 9.1.2.2.22.1.4.6

Add and .

Step 9.1.2.2.22.1.5

Rewrite as .

Step 9.1.2.2.22.1.5.1

Use to rewrite as .

Step 9.1.2.2.22.1.5.2

Apply the power rule and multiply exponents, .

Step 9.1.2.2.22.1.5.3

Combine and .

Step 9.1.2.2.22.1.5.4

Cancel the common factor of .

Step 9.1.2.2.22.1.5.4.1

Cancel the common factor.

Step 9.1.2.2.22.1.5.4.2

Rewrite the expression.

Step 9.1.2.2.22.1.5.5

Evaluate the exponent.

Step 9.1.2.2.22.2

Add and .

Step 9.1.2.2.22.3

Subtract from .

Step 9.1.2.2.23

Cancel the common factor of and .

Step 9.1.2.2.23.1

Factor out of .

Step 9.1.2.2.23.2

Cancel the common factors.

Step 9.1.2.2.23.2.1

Factor out of .

Step 9.1.2.2.23.2.2

Cancel the common factor.

Step 9.1.2.2.23.2.3

Rewrite the expression.

Step 9.1.2.2.24

Move the negative in front of the fraction.

Step 9.1.2.3

Find the common denominator.

Step 9.1.2.3.1

Multiply by .

Step 9.1.2.3.2

Multiply by .

Step 9.1.2.3.3

Multiply by .

Step 9.1.2.3.4

Multiply by .

Step 9.1.2.3.5

Reorder the factors of .

Step 9.1.2.3.6

Multiply by .

Step 9.1.2.3.7

Multiply by .

Step 9.1.2.4

Combine the numerators over the common denominator.

Step 9.1.2.5

Simplify each term.

Step 9.1.2.5.1

Apply the distributive property.

Step 9.1.2.5.2

Multiply by .

Step 9.1.2.5.3

Multiply by .

Step 9.1.2.5.4

Apply the distributive property.

Step 9.1.2.5.5

Multiply by .

Step 9.1.2.5.6

Multiply by .

Step 9.1.2.5.7

Apply the distributive property.

Step 9.1.2.5.8

Multiply by .

Step 9.1.2.5.9

Multiply by .

Step 9.1.2.5.10

Apply the distributive property.

Step 9.1.2.5.11

Multiply by .

Step 9.1.2.5.12

Multiply by .

Step 9.1.2.6

Simplify terms.

Step 9.1.2.6.1

Subtract from .

Step 9.1.2.6.2

Subtract from .

Step 9.1.2.6.3

Add and .

Step 9.1.2.6.4

Add and .

Step 9.1.2.6.5

Rewrite as .

Step 9.1.2.6.6

Factor out of .

Step 9.1.2.6.7

Factor out of .

Step 9.1.2.6.8

Move the negative in front of the fraction.

Step 9.2

Write the and coordinates in point form.

Step 10

Since the first derivative changed signs from positive to negative around , then there is a turning point at .

Step 11

Step 11.1

Find to find the y-coordinate of .

Step 11.1.1

Replace the variable with in the expression.

Step 11.1.2

Simplify .

Step 11.1.2.1

Remove parentheses.

Step 11.1.2.2

Simplify each term.

Step 11.1.2.2.1

Raising to any positive power yields .

Step 11.1.2.2.2

Raising to any positive power yields .

Step 11.1.2.2.3

Multiply by .

Step 11.1.2.2.4

Raising to any positive power yields .

Step 11.1.2.2.5

Multiply by .

Step 11.1.2.3

Simplify by adding numbers.

Step 11.1.2.3.1

Add and .

Step 11.1.2.3.2

Add and .

Step 11.2

Write the and coordinates in point form.

Step 12

Since the first derivative changed signs from negative to positive around , then there is a turning point at .

Step 13

Step 13.1

Find to find the y-coordinate of .

Step 13.1.1

Replace the variable with in the expression.

Step 13.1.2

Simplify .

Step 13.1.2.1

Remove parentheses.

Step 13.1.2.2

Simplify each term.

Step 13.1.2.2.1

Apply the product rule to .

Step 13.1.2.2.2

Raise to the power of .

Step 13.1.2.2.3

Use the Binomial Theorem.

Step 13.1.2.2.4

Simplify each term.

Step 13.1.2.2.4.1

Raise to the power of .

Step 13.1.2.2.4.2

Raise to the power of .

Step 13.1.2.2.4.3

Multiply by .

Step 13.1.2.2.4.4

Raise to the power of .

Step 13.1.2.2.4.5

Multiply by .

Step 13.1.2.2.4.6

Rewrite as .

Step 13.1.2.2.4.6.1

Use to rewrite as .

Step 13.1.2.2.4.6.2

Apply the power rule and multiply exponents, .

Step 13.1.2.2.4.6.3

Combine and .

Step 13.1.2.2.4.6.4

Cancel the common factor of .

Step 13.1.2.2.4.6.4.1

Cancel the common factor.

Step 13.1.2.2.4.6.4.2

Rewrite the expression.

Step 13.1.2.2.4.6.5

Evaluate the exponent.

Step 13.1.2.2.4.7

Multiply by .

Step 13.1.2.2.4.8

Multiply by .

Step 13.1.2.2.4.9

Rewrite as .

Step 13.1.2.2.4.10

Raise to the power of .

Step 13.1.2.2.4.11

Rewrite as .

Step 13.1.2.2.4.11.1

Factor out of .

Step 13.1.2.2.4.11.2

Rewrite as .

Step 13.1.2.2.4.12

Pull terms out from under the radical.

Step 13.1.2.2.4.13

Multiply by .

Step 13.1.2.2.4.14

Rewrite as .

Step 13.1.2.2.4.14.1

Use to rewrite as .

Step 13.1.2.2.4.14.2

Apply the power rule and multiply exponents, .

Step 13.1.2.2.4.14.3

Combine and .

Step 13.1.2.2.4.14.4

Cancel the common factor of and .

Step 13.1.2.2.4.14.4.1

Factor out of .

Step 13.1.2.2.4.14.4.2

Cancel the common factors.

Step 13.1.2.2.4.14.4.2.1

Factor out of .

Step 13.1.2.2.4.14.4.2.2

Cancel the common factor.

Step 13.1.2.2.4.14.4.2.3

Rewrite the expression.

Step 13.1.2.2.4.14.4.2.4

Divide by .

Step 13.1.2.2.4.15

Raise to the power of .

Step 13.1.2.2.5

Add and .

Step 13.1.2.2.6

Add and .

Step 13.1.2.2.7

Add and .

Step 13.1.2.2.8

Cancel the common factor of and .

Step 13.1.2.2.8.1

Factor out of .

Step 13.1.2.2.8.2

Factor out of .

Step 13.1.2.2.8.3

Factor out of .

Step 13.1.2.2.8.4

Cancel the common factors.

Step 13.1.2.2.8.4.1

Factor out of .

Step 13.1.2.2.8.4.2

Cancel the common factor.

Step 13.1.2.2.8.4.3

Rewrite the expression.

Step 13.1.2.2.9

Apply the product rule to .

Step 13.1.2.2.10

Raise to the power of .

Step 13.1.2.2.11

Use the Binomial Theorem.

Step 13.1.2.2.12

Simplify each term.

Step 13.1.2.2.12.1

Raise to the power of .

Step 13.1.2.2.12.2

Multiply by by adding the exponents.

Step 13.1.2.2.12.2.1

Multiply by .

Step 13.1.2.2.12.2.1.1

Raise to the power of .

Step 13.1.2.2.12.2.1.2

Use the power rule to combine exponents.

Step 13.1.2.2.12.2.2

Add and .

Step 13.1.2.2.12.3

Raise to the power of .

Step 13.1.2.2.12.4

Multiply by .

Step 13.1.2.2.12.5

Rewrite as .

Step 13.1.2.2.12.5.1

Use to rewrite as .

Step 13.1.2.2.12.5.2

Apply the power rule and multiply exponents, .

Step 13.1.2.2.12.5.3

Combine and .

Step 13.1.2.2.12.5.4

Cancel the common factor of .

Step 13.1.2.2.12.5.4.1

Cancel the common factor.

Step 13.1.2.2.12.5.4.2

Rewrite the expression.

Step 13.1.2.2.12.5.5

Evaluate the exponent.

Step 13.1.2.2.12.6

Multiply by .

Step 13.1.2.2.12.7

Rewrite as .

Step 13.1.2.2.12.8

Raise to the power of .

Step 13.1.2.2.12.9

Rewrite as .

Step 13.1.2.2.12.9.1

Factor out of .

Step 13.1.2.2.12.9.2

Rewrite as .

Step 13.1.2.2.12.10

Pull terms out from under the radical.

Step 13.1.2.2.13

Add and .

Step 13.1.2.2.14

Add and .

Step 13.1.2.2.15

Cancel the common factor of and .

Step 13.1.2.2.15.1

Factor out of .

Step 13.1.2.2.15.2

Factor out of .

Step 13.1.2.2.15.3

Factor out of .

Step 13.1.2.2.15.4

Cancel the common factors.

Step 13.1.2.2.15.4.1

Factor out of .

Step 13.1.2.2.15.4.2

Cancel the common factor.

Step 13.1.2.2.15.4.3

Rewrite the expression.

Step 13.1.2.2.16

Apply the product rule to .

Step 13.1.2.2.17

Raise to the power of .

Step 13.1.2.2.18

Cancel the common factor of .

Step 13.1.2.2.18.1

Factor out of .

Step 13.1.2.2.18.2

Factor out of .

Step 13.1.2.2.18.3

Cancel the common factor.

Step 13.1.2.2.18.4

Rewrite the expression.

Step 13.1.2.2.19

Combine and .

Step 13.1.2.2.20

Rewrite as .

Step 13.1.2.2.21

Expand using the FOIL Method.

Step 13.1.2.2.21.1

Apply the distributive property.

Step 13.1.2.2.21.2

Apply the distributive property.

Step 13.1.2.2.21.3

Apply the distributive property.

Step 13.1.2.2.22

Simplify and combine like terms.

Step 13.1.2.2.22.1

Simplify each term.

Step 13.1.2.2.22.1.1

Multiply by .

Step 13.1.2.2.22.1.2

Move to the left of .

Step 13.1.2.2.22.1.3

Combine using the product rule for radicals.

Step 13.1.2.2.22.1.4

Multiply by .

Step 13.1.2.2.22.1.5

Rewrite as .

Step 13.1.2.2.22.1.6

Pull terms out from under the radical, assuming positive real numbers.

Step 13.1.2.2.22.2

Add and .

Step 13.1.2.2.22.3

Add and .

Step 13.1.2.2.23

Cancel the common factor of and .

Step 13.1.2.2.23.1

Factor out of .

Step 13.1.2.2.23.2

Cancel the common factors.

Step 13.1.2.2.23.2.1

Factor out of .

Step 13.1.2.2.23.2.2

Cancel the common factor.

Step 13.1.2.2.23.2.3

Rewrite the expression.

Step 13.1.2.2.24

Move the negative in front of the fraction.

Step 13.1.2.3

Find the common denominator.

Step 13.1.2.3.1

Multiply by .

Step 13.1.2.3.2

Multiply by .

Step 13.1.2.3.3

Multiply by .

Step 13.1.2.3.4

Multiply by .

Step 13.1.2.3.5

Reorder the factors of .

Step 13.1.2.3.6

Multiply by .

Step 13.1.2.3.7

Multiply by .

Step 13.1.2.4

Combine the numerators over the common denominator.

Step 13.1.2.5

Simplify each term.

Step 13.1.2.5.1

Apply the distributive property.

Step 13.1.2.5.2

Multiply by .

Step 13.1.2.5.3

Multiply by .

Step 13.1.2.5.4

Apply the distributive property.

Step 13.1.2.5.5

Multiply by .

Step 13.1.2.5.6

Multiply by .

Step 13.1.2.5.7

Apply the distributive property.

Step 13.1.2.5.8

Multiply by .

Step 13.1.2.5.9

Multiply by .

Step 13.1.2.5.10

Apply the distributive property.

Step 13.1.2.5.11

Multiply by .

Step 13.1.2.5.12

Multiply by .

Step 13.1.2.6

Simplify terms.

Step 13.1.2.6.1

Subtract from .

Step 13.1.2.6.2

Subtract from .

Step 13.1.2.6.3

Subtract from .

Step 13.1.2.6.4

Subtract from .

Step 13.1.2.6.5

Rewrite as .

Step 13.1.2.6.6

Factor out of .

Step 13.1.2.6.7

Factor out of .

Step 13.1.2.6.8

Move the negative in front of the fraction.

Step 13.2

Write the and coordinates in point form.

Step 14

These are the turning points.

Step 15