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05aut-f - MATH 51 FINAL EXAM Name Numeric Student ID TA and...

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MATH 51 FINAL EXAM December 12, 2005 Name: Numeric Student ID: TA and Section No.: I agree to abide by the terms of the honor code: Signature: Instructions: Print your name, and student ID number in the space provided. You may not use notes, or textbooks, or calculators. Read each question carefully. Some questions continue to more than one page. Correct answers without justification will receive little or no credit. There are 12 questions. There is a 3 hour time limit on this exam. Good luck. Question Score Maximum 1 10 2 10 3 10 4 10 5 10 6 15 7 10 8 10 9 10 10 10 11 10 12 5 Total 120

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Question 1 of 12, Page 2 of 17 Name: 1. Find all critical points of the function f ( x, y ) = 3 xy - x 2 y - 2 xy 2 . Determine the nature of the critical points (i.e. local min/local max/neither max nor min).
Question 2 of 12, Page 3 of 17 Name: 2. Compute the determinant - 2 1 1 - 1 1 - 2 - 1 1 1 - 1 - 2 1 - 1 1 1 - 2 .

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Question 3 of 12, Page 4 of 17 Name: 3. Consider the function f ( x, y ) = y x 2 . (a) Draw three different level sets of f . Briefly describe the shape of the resulting curves you find.
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