Math Is Fun Forum

renjer

Member

Registered: 2006-04-29

Posts: 50

Lagrange

Use Lagrange multipliers to find the minimum distance from the point (5,5,4) to the paraboloid z=4-x^2-y^2.

I know a lot about Lagrange multipliers, they're quite easy, but the problem is, how do you find the distance from a point in space to a surface?

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,413

Re: Lagrange

I don't know about Lagrange multipliers and read about it here.

If your problem requires finding the distance between a point and a surface, the distance required must be the shortest distance to the point from normal to the surface!

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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renjer

Member

Registered: 2006-04-29

Posts: 50

Re: Lagrange

Then how can I relate that to Lagrange multipliers? I know there is supposed to be 2 equations f(x,y,z) and g(x,y,z) but now I don't know which two equations can I use.

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: Lagrange

you can set up a distance function,
maximize it or its square under the constraint z=4-x^2-y^2.

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X'(y-Xβ)=0