Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**renjer****Member**- Registered: 2006-04-29
- Posts: 51

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?

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 12,919

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!

Character is who you are when no one is looking.

Offline

**renjer****Member**- Registered: 2006-04-29
- Posts: 51

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.

Offline

**George,Y****Member**- Registered: 2006-03-12
- Posts: 1,306

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**

Offline