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Unformatted text preview: whose components have the largest possible sum. (Find only the critical points.) Solution: Assume h x,y,z i is a vector in R 3 such that z 0 such that h x,y,z i = 16 and Sum = x + y + z . Solving for z from our constraint, we have h x,y,z i = 16 p x 2 + y 2 + z 2 = 16 z = p 16x 2y 2 Therefore, we have the function f ( x,y ) = x + y + p 16x 2y 2 to describe the sum. Dierentiating: f x ( x,y ) = 1 +x p 16x 2y 2 f y ( x,y ) = 1 +y p 16x 2y 2 If f x ( x,y ) = 0, then 16 = 2 x 2 + y 2 . If f y ( x,y ) = 0, then 16 = x 2 +2 y 2 . Solving the system, we nd that the points ( 4 3 , 4 3 ) (4 3 , 4 3 ) ( 4 3 ,4 3 ) (4 3 ,4 3 ) are critical points for f ....
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This note was uploaded on 12/15/2011 for the course MAC 2313 taught by Professor Keeran during the Spring '08 term at University of Florida.
 Spring '08
 Keeran
 Calculus, Geometry

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