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Use Lagrange Multipliers to Find the Maximum and Minimum Values f(x,y,z)=5x−y−5zf ( x , y , z ) = 5 x - y - 5 z

Question 121

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Use Lagrange multipliers to find the maximum and minimum values of the function f(x,y,z)=5x−y−5zf ( x , y , z ) = 5 x - y - 5 z subject to the constraints x+2y−z=0x + 2 y - z = 0 and x2+4y2=1x ^ { 2 } + 4 y ^ { 2 } = 1 .

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