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Unformatted text preview: Math 115 — Second Midterm November 24, 2009 Name: EXAM SOLUTIONS Instructor: Section: 1. Do not open this exam until you are told to do so. 2. This exam has 11 pages including this cover. There are 8 problems. Note that the problems are not of equal difficulty, so you may want to skip over and return to a problem on which you are stuck. 3. Do not separate the pages of this exam. If they do become separated, write your name on every page and point this out to your instructor when you hand in the exam. 4. Please read the instructions for each individual problem carefully. One of the skills being tested on this exam is your ability to interpret mathematical questions, so instructors will not answer questions about exam problems during the exam. 5. Show an appropriate amount of work (including appropriate explanation) for each problem, so that graders can see not only your answer but how you obtained it. Include units in your answer where that is appropriate. 6. You may use any calculator except a TI92 (or other calculator with a full alphanumeric keypad). However, you must show work for any calculation which we have learned how to do in this course. You are also allowed two sides of a 3 ′′ × 5 ′′ note card. 7. If you use graphs or tables to find an answer, be sure to include an explanation and sketch of the graph, and to write out the entries of the table that you use. 8. Turn off all cell phones and pagers , and remove all headphones. 9. Use the techniques of calculus to solve the problems on this exam. Problem Points Score 1 10 2 8 3 14 4 12 5 12 6 14 7 14 8 16 Total 100 Math 115 / Exam 2 (November 24, 2009) page 2 1 . [10 points] For each of the following statements, circle True if the statement is always true and circle False otherwise. a . [2 points] If j ′ ( x ) is continuous everywhere and changes from negative to positive at x = a , then j has a local minimum at x = a . True False b . [2 points] If f and g are differentiable increasing functions and g ( x ) is never equal to 0, then the function h ( x ) = f ( x ) g ( x ) is also a differentiable increasing function. True False c . [2 points] If k is a differentiable function with exactly one critical point, then k has either a global minimum or global maximum at that point. True False d . [2 points] If F and F ′ are differentiable functions and F ′′ (2) = 0, then F has a point of inflection at x = 2. True False e . [2 points] If f is a differentiable function with f ( a ) = b and f ′ is always positive, then f ′ ( a ) ( ( f − 1 ) ′ ( b ) ) = 1. True False Math 115 / Exam 2 (November 24, 2009) page 3 2 . [8 points] On the axes provided below, sketch the graph of a function f satisfying all of the following: • f is defined and continuous on ( −∞ , ∞ )....
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This note was uploaded on 05/15/2010 for the course MATH CALC 115 taught by Professor Reit during the Winter '09 term at University of Michigan.
 Winter '09
 REIT

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