math_112_test_3_winter_2011

math_112_test_3_winter_2011 - Math 112 Winter 2011 Exam 3...

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Unformatted text preview: Math 112, Winter 2011, Exam 3 Solutions Multiple Choice. 1. Find the absolute minimum of the function f ( x ) = x 2 / 3 on [- 2 , 3]. a)- 2 b)- 3 c) d) 3 4 e) 1 f) 3 9 Answer: c) 2. Find all the numbers c that satisfy the conclusion of the Mean Value Theorem for the function f ( x ) = 1 x on the interval [1 , 2]. a) c = 1 b) c = 2 c) c = 2 d) c = 2 , 3 e) c = 1 . 5 f) c = 1 . 5 , 3 Answer: c) The graph of the first derivative f of a function f is shown below. Use this graph for the next two problems. 8 4 y = f ( x ) x 5 7 9 2 1 3 y 6 3. The graph of the derivative f of a function f is shown above. On what intervals is the function f increasing? a) (0 , 1) (3 , 5) (7 , 8) b) (1 , 3) (5 , 7) (8 , 9) c) (0 , 2) (4 , 6) d) (2 , 4) (6 , 9) e) (2 , 4) (6 , 7 . 5) f) (0 , 2) (4 , 6) (7 . 5 , 9) Answer: c) 4. The graph of the derivative f of a function f is shown above. On what intervals is the function f concave upward? a) (0 , 1) (3 , 5) (7 , 8) b) (1 , 3) (5 , 7) (8 , 9) c) (0 , 2) (4 , 6) d) (2 , 4) (6 , 9) e) (2 , 4) (6 , 7 . 5) f) (0 , 2) (4 , 6) (7 . 5 , 9) Answer: a) 5. Find all inflection points of the function f ( x ) = 2 x 3 + 3 x 2- 36 x . a) x = 2 ,- 3 b) x =- 1 2 c) x = 0 , 1 2 d) x =- 2 , 3 e) x = 2 f) There arent any. Answer: b) 6. Evaluate the following limit lim x x + 2 ln(7 + 7 e x ) . a) 1 b) 2 7 c) d) 1 7 e) f) The limit DNE. Answer: a) 7. Find two positive numbers a and b whose product is 900 and whose sum is a minimum. What is a + b ? a) 51 b) 52 c) 55 d) 60 e) 65 f) 68 g) None of the above. Answer: d) 8. If f is an odd function with a local maximum at the point (2 , 1), which of the following is true? a) (- 2 , 1) is a local minimum. b) (- 2 ,- 1) is a local maximum. c) (- 2 , 1) is a local maximum. d) (- 2 ,- 1) is a local minimum....
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This note was uploaded on 02/09/2012 for the course MATH 112 taught by Professor Jarvis during the Winter '08 term at BYU.

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math_112_test_3_winter_2011 - Math 112 Winter 2011 Exam 3...

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