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**renjer****Member**- Registered: 2006-04-29
- Posts: 50

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?

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 27,000

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!

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**renjer****Member**- Registered: 2006-04-29
- Posts: 50

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.

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**George,Y****Member**- Registered: 2006-03-12
- Posts: 1,333

you can set up a distance function,

maximize it or its square under the constraint z=4-x^2-y^2.

**X'(y-Xβ)=0**

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