What are the gradient and the determinant of the Hessian of the function f(x, y ) = x2 y 2 at its global optimum?

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Question:

What are the gradient and the determinant of the Hessian of the function f(x, y ) = x2 y 2 at its global optimum?

A.

∇f = 0i + 0j and h > 0

B.

∇f = 0i + 0j and h = 0

C.

∇f = 1i +1j and h < 0

D.

∇f = 1i +1j and h = 0

Answer» a. ∇f = 0i + 0j and h > 0

Note: The above multiple-choice question is for all general and Competitive Exams in India.