The method of Lagrange multipliers assumes that the extreme values exist, but that is not always the case Show that the problem of finding the minimum value of f (x, y) x 2 y 2 subject to the constraint xy 1 can be solved using Lagrange multipliers, but f does not have a maximum value with that con...

x y x y gx y xy 1 and VfXVg 2x 2y Ay Ax so 2x Ay 2y x and xy 1 From the last equation a ...

The method of Lagrange multipliers assumes that the extreme values exist, but that is not always the

Question:

The method of Lagrange multipliers assumes that the extreme values exist, but that is not always the case. Show that the problem of finding the minimum value of f (x, y) = x² + y² subject to the constraint xy = 1 can be solved using Lagrange multipliers, but f does not have a maximum value with that constraint.

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