I have a set $\{z<\sqrt{x^2+y^2}\}$ and I have to find the max and min distance between the set and a point. I don't understand why the Lagrange multiplier method doesn't work when the max and min are in the origin $(0,0,0)$. Are there another methods?
Why is not possible to find max and min with Lagrange multiplier in the corner of a set?
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0What is at the origin? Is it the point $(x,y,z)$ at which the distance is minimized? Lagrange should work, provided distances on the boundary of the region are checked separately, but only if the region is a subset of a compact part of 3-space. I don't think your region has this property since as stated $z$ can be any negative real. – 2017-02-17
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0Why, Lagrange cannot be applied to a corner of the set? For example in the peak of a cone – 2017-02-17
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0I think I have the answer now. The function must be differenziable in the point. – 2017-02-17