math10c fall 2009 real final!!

# math10c fall 2009 real final!! - Math 10C Fall 2009 Final...

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Math 10C - Fall 2009 - Final Exam Name: Student ID: Section time: Instructions: Please print your name, student ID and section time. During the test, you may not use books or telephones. You may use a ”cheat sheet” of notes which should be a page, front only. Read each question carefully, and show all your work. Answers with no explanation will re- ceive no credit, even if they are correct. There are 10 questions which are worth 150 points. You have 180 minutes to complete the test. Question Score Maximum 1 15 2 20 3 13 4 17 5 15 6 15 7 15 8 15 9 10 10 15 Total 150

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Problem 1. [ 15 points ] At what point ( x,y,z ) on the plane x + 2 y - z = 5 does the minimum of the function f ( x,y,z ) = x 2 + 2 y 2 + ( z + 1) 2 occur?
Problem 2. [ 20 points. ] Consider the function f ( x,y ) = 3 y 2 - 2 y 3 - 3 x 2 + 6 xy. (i) [8] Find the critical points of the function.

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(ii) [8] Determine the nature of the critical points (local min/local max/saddle).
(iii) [4] Does the function f ( x,y ) have a global minimum or a global maximum?

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Problem 3.
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math10c fall 2009 real final!! - Math 10C Fall 2009 Final...

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