Determining Max And Min Values

Question 1

How do we find relative maximum or minimum

Answer 1

First and Second Derivative Test

Question 2

Which test should you always try first when finding relative max or min values?

Answer 2

Second Derivative Test

Question 3

What are the tests for determining min and max values

Answer 3

Candidate Test
First Derivative Test
Second Derivative Test

Question 4

When do we use candidates test

Answer 4

When finding extreme max and min values

Question 5

When do we use first derivative test

Answer 5

When finding relative max and min values

Question 6

How do we find extreme maximum or minimum

Answer 6

Candidate Test

Question 7

What are the steps in the Candidate Test

Answer 7

Steps:

1. Differentiate function
2. Equate to 0 (just add =0 at the end)
3. Simplify if needed (may use factorization)
4. Solve to find critical point
5. Plug in endpoints (interval) a and b and critical value c into f(x) NOT THE DIFFERENTIATED EQUATION
6. Compare results. The point with the largest value is maximum. The smallest is minimum

Question 8

What are the steps in the First Derivative Test

Answer 8

Steps:
1. Differentiate
2. Equate derivative to 0
3. Solve for critical point (c)
4. Choose a number less than c, (a) and more then c, (b)
5. Plug in a and b into the derivative equation
6. If f’(a) is negative and f’(b) is positive c is a minimum
If f’(a) is positive and f’(b) is negative, c is a maximum

Question 9

What are the steps in the Second Derivative Test

Answer 9

Steps:
1. Differentiate f(x)
2. Equate to 0
3. Solve to find critical point c
4. Differentiate f’(x)
5. Plug critical value c into f’’(x)
6. Solve
7. If f’’(c) is negative, c is a maximum
If f”(c) is positive, c is a minimum

Question 10

When do we use the First Derivative Test INSTEAD OF the Second Derivative Test

Answer 10

When the first and second derivative in the Second Derivative Test are 0