(b) Find the extreme values of the function g(x,y) = 2xy + 2x² - 4 on the region described by the inequality x² + y² ≤4.
(b) Find the extreme values of the function g(x,y) = 2xy + 2x² - 4 on the region described by the inequality x² + y² ≤4.
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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Transcribed Image Text:Question 3
(a)
(b)
Apply Lagrange Multipliers to find the maximum and minimum of the func-
tion
subject to the constraint
f(x, y, z)=exyz
x²+2y² +3z² = 6.
Find the extreme values of the function
g(x,y)=2xy + 2x²-4
on the region described by the inequality
x² + y² ≤4.
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