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Problem 1 a x y D x y dxdy b where D x y x 0 y 0 and x y 1 2 x 3 y 1 dxdy D where D x y x 2 y 2 4 2 x 3 y 1 dxdy 1 dxdy 4 D D Problem 2 Problem 3 Problem 4 iii Let Df x 0 we have following equations 4 x1 x2 0 x1 3 x3 0 3x 2 x 2 3 1 9 Solve 1 9 and obtain the only one critical point x1 x2 x3 0 0 0 4 1 0 D f 0 0 0 1 0 3 0 3 2 2 The eigenvalues of D f 0 0 0 are 4 2045 1 8624 and 4 3421 It is not a positive definite matrix and not negative definite Therefore x1 x2 x3 0 0 0 is not an extremum point 2
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