QUIZ #10: CALCULUS 1A (Stankova) Wednesday, April 7, 2004 Section 10:00–11:00 (Voight)

Name:

Please complete the following problem(s) in the space provided. You may not use a calculator. You will have 15 minutes to complete the quiz.

Please include all relevant intermediate calculations and explain your work when appropriate.

Problem 1. Find two numbers whose product is 4 and for which the sum of their squares is a minimum.

QUIZ #10: CALCULUS 1A (Stankova) Wednesday, April 7, 2004 Section 11:00–12:00 (Voight)

Name:

Please complete the following problem(s) in the space provided. You may not use a calculator. You will have 15 minutes to complete the quiz.

Please include all relevant intermediate calculations and explain your work when appropriate.

Problem 1. Consider the cost function

C(x) = 16 + x^{3}.

given in millions of dollars.

(a) At what production level x is the average cost minimal?

(b) Let

p(x) = 36 − 3x − x^{2}

be the demand function. At what production level x is the profit maximal? What is the maximum profit?