Problem 1(a) where {( , ) | 0, 0, and 1}Dx ydxdy D x y x y x yx y (b) 2 22 3 1 where {( , ) | 4}Dx y dxdy D x y x y 2 3 1 = 1 = - 4D Dx y dxdy dxdy Problem 2Problem 3Problem 41 21 32 3(iii) Let ( ) 0, we have following equations4 0 3 0 (1.9)3 2Solve (1.9) and obtain the only one critical point Df xx xx xx x 1 2 322 ( , , )=(0,0,0)4 1 0 (0,0,0) 1 0 30 3 2The eigenvalues of (0,0,0) are -4.2045, 1.8624, and 4.3421. It is not a positive definite matrix and not negativedefinite. Therx x xD fD f 1 2 3efore, ( , , )=(0,0,0) is not an extremum point.x x
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