Question: Let f ( x , y ) = x y ( 1 x y ) . Find the discriminate D ( x , y )

Let f(x,y)=xy(1xy).

  1. Find the discriminate D(x,y)=fxx(x,y)fyy(x,y)fxy2(x,y).
  2. The function f(x,y) has four critical points (0, 0), (1, 0), (0, 1) and ( 1 3 , 1 3 ). Use the Second Derivative Test to determine each critical point is a saddle point, local minimum or local maximum point.

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