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Unformatted text preview: g ( x, y, z ) = k. 2. Evaluate f at all of the points ( x, y, z ) that result from step 1. The largest of these values is the maximum of f subject to the constraint; the smallest of these values is the minimum of f subject to the constraint. Example 15.8.1 Redo fnding the absolute extrema oF f ( x, y ) = x 2 + 2 y 2x on the region x 2 + y 2 ≤ 4 using the Method oF Lagrange Multipliers. Example 15.8.2 ±ind the extrema oF f ( x, y ) = xy iF ( x, y ) is restricted to the ellipse 4 x 2 + y 2 = 4 . Example 15.8.3 IF f ( x, y, z ) = 4 x 2 + y 2 + 5 z 2 , fnd the point on the plane 2 x + 3 y + 4 z = 12 at which f ( x, y, z ) has its least value. 33...
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This note was uploaded on 10/11/2010 for the course MTHSC 206 taught by Professor Chung during the Fall '07 term at Clemson.
 Fall '07
 Chung
 Derivative, Multivariable Calculus

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