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Unformatted text preview: Name: PID: Discussion Section No: Time: TAs name: Quiz 4, Math 20C  Lecture D (Fall 2007) Duration: 20 minutes Please close all your notes and books, turn off your phones and put them away. To get full credit you should support your answers. 1. (5 points) Find the absolute maximum and minimum values of f ( x, y ) = x 4 + y 4 4 xy +2 on the set D = { ( x, y ) : 0 x 3 , y 2 } . Solution. First, find the critical points. This is done by solving the system f x ( x, y ) = f y ( x, y ) = 0. Since f x ( x, y ) = 4 x 3 4 y and f y ( x, y ) = 4 y 3 4 x , the previous system is equivalent to the system y = x 3 and x = y 3 . Substituting y from the first equation into second, we get x = y 3 = ( x 3 ) 3 = x 9 which implies 0 = x 9 x = x ( x 8 1). This means that x = 0 or x 8 = 1. The equation x 8 = 1 implies that x = 1 or x = 1. If x = 0, we get y = 0 3 = 0. If x = 1 we get y = ( 1) 3 = 1. If x = 1, we get y = 1 3 = 1. Thus, the solutions of the system= 1....
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This note was uploaded on 04/29/2008 for the course MATH 20C taught by Professor Helton during the Fall '08 term at UCSD.
 Fall '08
 Helton
 Math

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