Charactertizing extrema

A point (x0, y0) is a critical point of f(x, y) if
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A critical point occurs where ∇ f(x, y) = 0. Which of the following represents the condition?
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For F(x, y) = [f(x, y), g(x, y)], the Jacobian matrix is
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The Hessian matrix of f(x, y) consists of
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