Question: Suppose that V is open in R2, that (a, b) V, and that f: V R has second-order total differential on V with

Suppose that V is open in R2, that (a, b) ∈ V, and that f: V → R has second-order total differential on V with fx(a, b) = fy(a, b) = 0. If the second-order partial derivatives of f are continuous at (a, b) and exactly two of the three numbers fxx(a, b), fxy(a, b), and fyy(a, b) are zero, prove that (a, b) is a saddle point if fxy(a, b) ≠ 0.

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If f xy a b 0 then f xx a b f yy a b 0 and it follows that D 2 fa b f xy a b hk takes both positive ... View full answer

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