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find the extrema of f(x, y) = xy on the ellipse x^2/8+y^2/2 =1.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Use Lagrange multipliers to (a) find the extrema of f(x, y) = xy on the ellipse x^2/8+y^2/2 =1. (b) find the extrema of f(x, y, z) = x − 2y + 5z on x^2+ y^2+ z^2= 30. (c) maximize
f(x, y, z) = x^2 + 2y − z^2
subject to the constraints 2x − y = 0 and y + z = 0 .

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