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Old Final (2003 Sp)

# Old Final (2003 Sp) - FINAL EXAM CALCULUS FOR THE SOCIAL...

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Math 52-10 FINAL EXAM CALCULUS FOR THE SOCIAL AND MANAGEMENT SCIENCES Spring 2003 May 12, 1:30 to 3:30 There are 9 questions in all; together they are worth 110%. Youmay chooseto do any, or all, of these questions. The value of each question, as a percentage, is denoted. Please be clear and precise in your solutions. I recommend that you display all your working. Do not write on the exam paper; write all your solutions in the blue books provided. 1. The followingis the graphof a function y = f(x), use it to determine: (a) The sign-chart of the functiony = f(x) (b) The sign-chartof thederivative y' = f'(x) (c) The sign-chartofthe secondderivative y" = f"(x) Do not provide any explanation. 10% GRAPH AS IN OUR MIDTERM, PROBLEM 1 continued ... 1

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2. Ona largeandneatdiagram,sketchthegraphof anyfunction y = f(x) with the following characteristics: . A horizontal asymptote at y = 2 . Two vertical asymptotes at x = - 2 and x = 4 . Onex-interceptat x = -1 . The following is the sign-chart of the derivative y': + I + I + -2 0 I - I + I - 467 Draw a large, careful diagram; do not provide any explanation.
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