Fall 2007 - Cioaba's Class - Quiz 4

Fall 2007 - Cioaba's Class - Quiz 4 - Name: PID: Discussion...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

This note was uploaded on 04/29/2008 for the course MATH 20C taught by Professor Helton during the Fall '08 term at UCSD.

Page1 / 2

Fall 2007 - Cioaba's Class - Quiz 4 - Name: PID: Discussion...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online