(Note this is not the same problem as last week's Problems of the Week ) Suppose that f(x, y) is a function such that fx 0, fy 0, fxx 0, fyy 0, and fay 0 on the region R (x, y) 0 x 4,0 y 4 For each pair of quantities in the following table, decide whether the quantity in Column A is greater, the quantity in Column B is greater, the two quantities are the same, or it cannot be determined which quantity (if any) is greater If it cannot be determined which quantity is greater, then give specific examples of functions for which the answer would be different that is, give a function f for which, say, the quantity in Column A is greater than the quantity in Column B, and another function g for which this is not true (Of course, your functions should satisfy the given conditions in the region be sure to include those computations ) Column A f(3,2) f(2, 2) f(1,1) f(3,3) f(3,2) f(3,2) f(2, 2) Column B (2,3) f(2, 2) (2, 2) f(3,2) f(3,1) f(3, 1) f(2,1)

Question: (Note: this is not the same problem as last week's Problems of the Week.) Suppose that f(x, y) is a function such that fx

(Note: this is not the same problem as last week's Problems of the Week.) Suppose that f(x, y) is a function such that fx < 0, fy > 0, fxx > 0, fyy > 0, and fay

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