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(b) Consider the function g(x, y) = x² + 2xy + 2xy². (i) Show that (0, 0) is a critical point and find any other critical point(s) of g. (ii) Classify the critical point (0, 0) of g(x, y) as a local maximum, a local minimum or a saddle. (iii) Is g(0, 0) a global maximum of g(x, y), a global minimum of g(x, y) or neither? Justify your answer

(b) Consider the function g(x, y) = x² + 2xy + 2xy². (i) Show that (0, 0) is a critical point and find any other critical point(s) of g. (ii) Classify the critical point (0, 0) of g(x, y) as a local maximum, a local minimum or a saddle. (iii) Is g(0, 0) a global maximum of g(x, y), a global minimum of g(x, y) or neither? Justify your answer

Advanced Engineering Mathematics
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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Hi, I have a differential equations question to ask. Thanks.
(b) Consider the function g(x, y) = x² + 2xy + 2xy². (i) Show that (0, 0) is a critical point and find any other critical point(s) of g. (ii) Classify the critical point (0, 0) of g(x, y) as a local maximum, a local minimum or a saddle. (iii) Is g(0,0) a global maximum of g(x, y), a global minimum of g(x, y) or neither? Justify your answer.
Transcribed Image Text:(b) Consider the function g(x, y) = x² + 2xy + 2xy². (i) Show that (0, 0) is a critical point and find any other critical point(s) of g. (ii) Classify the critical point (0, 0) of g(x, y) as a local maximum, a local minimum or a saddle. (iii) Is g(0,0) a global maximum of g(x, y), a global minimum of g(x, y) or neither? Justify your answer.
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