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Exam 2 Math 1100 Name: \<ey 1 November, 2013 UID: Instructions: • Answer each question in the space provided. • No calculators are allowed. • Show all work. Answers not supported by appropriate work will not receive credit; partial credit will be given for progress towards a solution. Page Points 2 16 3 8 4 27 5 24 6 25 Total: 100 Score Math 1100 Exam 1, Page 2 of 6 For questions 1-4, assume the graph below represents 25 September, 2013 f(x). / 10 - 0 .5 .10 1. (4 points) Point A is: 3. (4 points) At point A, A. A relative maximum positive relative minimum B. negative C. A horizontal point of inflection f” is: C. zero D. None of the above 4. (4 points) At point B, the graph is: 2. (4 points) At point A, f’(x) is: A. increasing and concave up A. positive ncreasing and concave down B. negative C. decreasing and concave up zero ID. decreasing and concave down Math 1100 Exam 1, Page 3 of 6 25 September, 2013 For questions 5 and 6, assume the graph below represents f’(x). y A D 5. (4 points) Which point corresponds to a maximum of represents f’(x)) f(x)? (Remember the graph Point A B. Point B C. Point C D. Point D E. None of the above 6. (4 points) At point D, the graph of f() A. increasing and concave up B. increasing and concave down decreasing and concave up D. decreasing and concave down (not the graph of f’(x)) is: Math 1100 7. Find Exam 1, Page 4 of 6 for each relation. Your answers should be simplified enough to be easily readable. (a) (9 points) y 2 + 2) ln(2x = d (b) (9 points) y = er+1 c.lI ‘-‘ K , • I (x+) — I () (x+ I) (x÷i )Z. (c) (9 points) y 2 x K 25 September, 2013 )ç X)1 2 4 2.4 xy 2 3 ‘C -—)2 x = 2y + 3x +4 Math 1100 Exam 1, Page 5 of 6 2.5 September, 2013 8. A company can produce x children’s Batman costumes at cost C(x) revenue function from selling x Batman costumes is R(x) 16i = 5 + 15x. The — (a) (18 points) How many Batmall costumes should the company produce to maximize profit? Rx I (ç ) CO1 cc4 ye d ow vhlc4yI’krnivll OCt’c.4 XHoOX 1— ?‘(x) 4&) 0 (b) (6 points) What is the maximum possible profit for the company? P(SO)= Lj 5 _ I 17-e r- bre 4 c.’ IViath 1100 Exam 1, Page 6 of 6 25 September. 2013 9. (25 points) •The volume of a spherical pumpkin is increasing at the rate of 4 in /day. 3 How fast is the radius of the pumpkin increasing when the radius is 5 inches? (Note: the volume of a sphere is given by V = ur ). 3 v (3 d€ mr-. k dy a9 LI Ar 25w