Define the function f: R? → R by f (x, y) = 2xy² – y² – 2x². a) Find the critical points of f. b) Show that ƒ attains a local maximum at (0,0). (c) Does ƒ have a global maximum?
Define the function f: R? → R by f (x, y) = 2xy² – y² – 2x². a) Find the critical points of f. b) Show that ƒ attains a local maximum at (0,0). (c) Does ƒ have a global maximum?
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:Define the function f: R² → R by
f (x, y) = 2xy² – y² – 2x².
(a) Find the critical points of f.
(b) Show that f attains a local maximum at (0,0).
(c) Does f have a global maximum?
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