1. Let f : R? → R be a function with continuous partial derivatives at least up to the second order. Consider the function h : R? → R : (x, y) → (x – 2y) f(x², y³). It is known that f(4, 1) = 0, Dif(4,1) > 0 and D2f(4, 1) > 0. Which of the following statements is true? (A) The function h has a local minimum at (2, 1). (B) The function h has a local maximum at (2, 1). (C) The function h has a saddle point at (2,1). (D) None of the previous statements is true.

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