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Unformatted text preview: Math 115 Final Exam December 18, 2006 Name: Instructor: Section Number: 1. Do not open this exam until you are told to begin. 2. This exam has 8 pages including this cover. There are 7 questions. 3. Do not separate the pages of the exam. If any pages do become separated, write your name on them and point them out to your instructor when you turn in the exam. 4. Please read the instructions for each individual exercise carefully. One of the skills being tested on this exam is your ability to interpret questions, so instructors will not answer questions about exam problems during the exam. 5. Show an appropriate amount of work for each exercise so that the graders can see not only the answer but also how you obtained it. Include units in your answers where appropriate. 6. You may use your calculator. You are also allowed two sides of a 3 by 5 notecard. 7. If you use graphs or tables to obtain an answer, be certain to provide an explanation and sketch of the graph to show how you arrived at your solution. 8. Please turn off all cell phones and pagers and remove all headphones. Problem Points Score 1 12 2 24 3 12 4 10 5 10 6 16 7 16 Total 100 2 1. (3 points each) In each of the following, circle one of the answers (A)-(E). No explanation neces- sary. (a) If f is differentiable for all x and has a local maximum at x = 3, then which of the following must be true? I. f (3) = 0 II. f (3) < III. f is continuous at x = 3 (A) I only (B) II only (C) I and II only (D) I and III only (E) I, II, and III (b) If f and g are differentiable, h ( x ) = f ( x )- g (...
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