Chapter 3 Test

Question 1

Extreme Value Theorem

Answer 1

If f is continuous on an interval then f has both an absolute minimum and maximum

Question 2

Extrema

Answer 2

Maximum/Minimum

Question 3

Critical Value

Answer 3

Possible location of a turning point or sharp turn, IT MUST BE IN THE DOMAIN OF THE FUNCTION. Critical values are where the derivative of the function is undefined or 0. Critical values are never on endpoints

Question 4

When do relative extrema occur?

Answer 4

Only at critical numbers NEVER AT ENDPOINTS

Question 5

When do absolute extrema occur?

Answer 5

At critical numbers or endpoints

Question 6

Candidates Test

Answer 6

Finds absolute extrema
1) Find the critical values(do the derivative of the function and find its zeroes or undefined values)
2) Plug the critical values into the original equation and do the same for the endpoints
3) Determine the absolute extrema

Question 7

How do you write extrema?

Answer 7

Abs/Relative Max/Min of ____ at x= _____

Question 8

Rolle’s Theorem

Answer 8

If f is continuous and differentiable on an interval, and two inputs have the same output there is at least one turning point in the interval

Question 9

How do you solve a Rolle’s Theorem problem?

Answer 9

Find the derivative of the function and make sure that is all real numbers if so then the function is differentiable. Also make sure that f is continuous by checking the domain of the original function. Then, plug in the endpoints of the interval to see if you have two inputs that get the same output, if so go look for your f’(c)=0

Question 10

Mean Value Theorem

Answer 10

If f is continuous and differentiable then there is at least one x=c that f’(c)= f(b)- f(a) all over b- a