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Department of Computer & Mathematical Sciences

MATA32

Quiz 4

Fall 2021

Instructions:

1. Use your UToronto email address to email the following directly to your TA, not Professor

    Grinnell and not via Quercus:

(a) Your first name(s) and last name as we use them in Canada, your student number, and

      your tutorial number;

(b) Your letter answers to the multiple choice and true-false questions. Make your letter

      answers clear. Use T and F for true and false, respectively. You are not to show any

      rough work in your answers.

2. You have 60 minutes to email your multiple choice and true false answers to your TA (not

    Professor Grinnell, not via Quercus). Your TA must receive your answers by 9:00 pm on

Sunday November 14. This is independent of where in the world you are located now.

3. The points per question are given. The entire quiz is out of 40. There are no part marks. 

Questions: (there are 5 multiple choice questions and 5 true/false questions.)

1. [4 points] A manufacturer’s total cost function is given by , where  is the total cost of producing  units. At what level of output will average cost per unit be a minimum? What is this minimum?  

(A) At output level, the minimum average cost is 23.             

(B) At output level, the minimum average cost is 4.                          

(C) At output level, the minimum average cost is 40.             

(D) At output level, the minimum average cost is 2.             .

2. [4 points] For the function , which of the following best describes its interval(s) of increasing and decreasing?

(A) The function is increasing on the entirety of its domain.

(B)  are the intervals of increasing,  is the interval of decreasing.

(C)  are the intervals of increasing,  is the interval of decreasing.

(D) The function is decreasing on the entirety of its domain.

3. [4 points] 2. For a monopolist, the cost per unit of producing a product is $3, and the demand equation is . What price gives the greatest profit?

(A) p=$6

(B) p=$60

(C) p=$16

(D) There is no such thing as the greatest profit because the profit can always go higher.

4. [4 points] For the function  on the closed interval [3,4], which of the following best describes the global maximum and minimum values of the function?

(A) Global minimum at x=4, global maximum at x=3.

(B) Global minimum at x=2, there is no global maximum.

(C) Global minimum at x=2, global maximum at x=4.

(D) Global minimum at x=3, global maximum at x=4.

5. [4 points] For the function , which of the following statement is true?

(A)  has an inflection point at  and the function changes from concave up to concave down through this point.

(B)  does not have an inflection point, but changes from concave down to concave up at .

(C)  is concave up on its domain.

(D)  does not have an inflection point, but changes from concave up to concave down at .

“True” or “False” questions (Use T and F for true and false, respectively.):

6. [4 points] “While looking for critical values of , we only take the value(s) that make .” Is this statement true or false?

7. [4 points] “If the first derivative test and the second derivative test both conclude that a critical point is a relative maximum, then by the closed interval method, this point must also be an absolute maximum.” Is this statement true or false?

8. [4 points] “Too many iterations of the Newton’s Method will sometimes cause the estimated values of the root to move further away from the actual value of the root.” Is this statement true or false?

9. [4 points] “If  changes concavity at , then there is a inflection point at ” Is this statement true or false?

10. [4 points] “The technique of Higher-Order Implicit differentiation can only be applied to find higher order derivatives of implicitly defined functions.” Is this statement true or false?