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(1) Consider the scalar function on the region 2 - y² - z² +xy f(x, y, z)= 1-x² - M = {(x, y, z) : 2x² +2y² + z² ≤ 4}. (a) Find the critical points of f in the interior of M and classify them as local min, local max or saddle pt. (b) Now use the method of Lagrange multipliers to find the maximum and minimum values of f in the whole region M, listing all points at which those values occur.

(1) Consider the scalar function on the region 2 - y² - z² +xy f(x, y, z)= 1-x² - M = {(x, y, z) : 2x² +2y² + z² ≤ 4}. (a) Find the critical points of f in the interior of M and classify them as local min, local max or saddle pt. (b) Now use the method of Lagrange multipliers to find the maximum and minimum values of f in the whole region M, listing all points at which those values occur.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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(1) Consider the scalar function on the region ƒ(x, y, z) = 1 − x² − y² − z² + xy M = {(x, y, z) : 2x² + 2y² + z² ≤ 4}. (a) Find the critical points of f in the interior of M and classify them as local min, local max or saddle pt. (b) Now use the method of Lagrange multipliers to find the maximum and minimum values of f in the whole region M, listing all points at which those values occur.
Transcribed Image Text:(1) Consider the scalar function on the region ƒ(x, y, z) = 1 − x² − y² − z² + xy M = {(x, y, z) : 2x² + 2y² + z² ≤ 4}. (a) Find the critical points of f in the interior of M and classify them as local min, local max or saddle pt. (b) Now use the method of Lagrange multipliers to find the maximum and minimum values of f in the whole region M, listing all points at which those values occur.
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