a5 - ) = x 2 + 2 x 2 y + y 2 . a) Use the method of...

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Math 237 Assignment 5 Due: Friday, June 27th 1. Find and classify the critical points of the following functions and determine the shape of the level curves near each critical point. a) f ( x, y ) = x 2 y - 2 xy 2 + 3 xy + 4. b) g ( x, y ) = xye 2 x +3 y . c) h ( x, y ) = 3 x 2 y + y 3 - 3 x 2 - 3 y 2 + 2. 2. Find the maximum and minimum of f ( x, y ) = x 2 + x + 3 y 2 + 3 on the region bounded by y = x + 1, y = 1 - x , y = x - 1, y = - x - 1. 3. Find the maximum and minimum of f ( x, y ) = 2 x 2 + x + y 2 - 2 on the region R = { ( x, y ) | x 2 + y 2 4. 4. Find the points on the surface z 2 = xy + 1 that are closest to the origin. 5. Let f ( x, y
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Unformatted text preview: ) = x 2 + 2 x 2 y + y 2 . a) Use the method of Lagrange multipliers to nd the maximum and minimum points of f ( x, y ) on the curve y = 4-x 2 . b) Let R be the region bounded by the curve y = 4-x 2 and the x-axis. Find the maximum and minimum value of f ( x, y ) on the region R . 6. Find the maximum and minimum values of f ( x, y ) = x on the piriform curve dened by y 2 + x 4-x 3 = 0....
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This note was uploaded on 04/18/2010 for the course MATH 237 taught by Professor Wolczuk during the Spring '08 term at Waterloo.

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