Consider the function f(x, y) = x2 + 3y2 + 2y on the closed disk S: x2 + y2 < 1. a) Find the critical points in the interior of S using the first and second derivative tests, and decide if they are local maxima, minima, or neither. b) Find the maximum and minimum of f(x, y) on the boundary of S by using Lagrange multipliers on the boundary of S. (i.e. optimize f(x, y) subject to the constraint x2 + y2 = 1). (c) Using the results of (a) and (b), conclude what the global maximum and minimum values of f(x, y) are, and where they are attained.

Consider the function f(x, y) = x2 + 3y2 + 2y on the closed disk S: x2 + y2 < 1. a) Find the critical points in the interior of S using the first and second derivative tests, and decide if they are local maxima, minima, or neither. b) Find the maximum and minimum of f(x, y) on the boundary of S by using Lagrange multipliers on the boundary of S. (i.e. optimize f(x, y) subject to the constraint x2 + y2 = 1). (c) Using the results of (a) and (b), conclude what the global maximum and minimum values of f(x, y) are, and where they are attained.

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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