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?

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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?
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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