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

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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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