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fr1241spring2001

# fr1241spring2001 - MATH COMMON FREE 1241 FINAL EXAMINATION...

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MATH 1241 COMMON FINAL EXAMINATION FREE RESPONSE SECTION SPRING 2001 This exam is divided into two parts. These pages contain Part II which consists of 6 free response questions. Please show all of your work on the problem. We will not grade loose paper . If you are basing your answer on a graph on your calculator, sketch a picture of your graph on your sheet and be sure to label your window. . Make sure that your name appears on each page. . At the end of the examination you MUST hand in this test booklet and all scratch paper . FREE RESPONSE SCORE: Name: Student No: Instructor: Section No:

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10 Part II. 1. For a certain function f, the following information is known: (i} f has continuous first and second derivatives on ( -00,00}; (ii) f'(x) > 0 on ( -00,0), f'(x) < 0 on (0,2), and f'(x) > 0 on (2,00); f"(x) > O on -00, -1), f"(x) < O on -1, 1), and f"(x) > O on (1, 00); J( -1) = 1, !(0) = 3, !(1) = 1, and !(2) = 0; and - (v) Jim f(x) = -1 and Jim f(x) = 00. :r;-+~oo :r;-+oo Use this information to answer the following questions. (a) Find the local maxima and local minima (if any) of I.
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