Consider the function f(x, y) = 4xy - 2x^4 - y^2. (a) Find the critical points of f. (b) Use the second partials test to classify the critical points. (c) Show that f does not have a global minimum.
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Key Concepts
Recommended Videos
Show that $ f(x, y) = x^2 + 4y^2 - 4xy + 2 $ has an infinite number of critical points and that $ D = 0 $ at each one. Then show that $ f $ has a local (and absolute) minimum at each critical point.
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