Can somebody tell me if I've started this off right?

I need to use the Lagrange method to find the minimum distance from the point (1,2,3) to any point of the surface:

Let:

and

and then just carry on in the usual manner?

Printable View

- Oct 18th 2009, 12:01 PMbillymMinimum Distance
Can somebody tell me if I've started this off right?

I need to use the Lagrange method to find the minimum distance from the point (1,2,3) to any point of the surface:

Let:

and

and then just carry on in the usual manner? - Oct 18th 2009, 04:00 PMtonio
- Oct 18th 2009, 05:44 PMbillym
I can see that... so what is the problem with my method?

...(1)

...(2)

...(3)

Plug (1) to (3) into the constraint:

Which gives

So:

- Oct 18th 2009, 06:01 PMtonio
- Oct 18th 2009, 06:11 PMbillym
I see. I suppose this will explain my other wrong answers. I have about ten example questions from my notes and they all involve plus signs. How do you determine if its plus or minus? (obviously I've stopped visualizing it at this point)

- Oct 19th 2009, 12:43 PMbillym
I've looked at a bunch of Lagrange tutorials, but they're all so different. I'm sure these basic questions aren't too difficult, but I seem to be stuck.

The question i am trying solve is:

Using the Lagrange multiplier method, find the minimum distance from the point (1,2,3) to any point on the surface defined by:

Every example that I have tells me that I should solve like this:

We have:

...(and so on)

...(and so on)

...(and so on)

Why do I not get the right answer unless I use in these equations? (Headbang) - Oct 19th 2009, 12:59 PMbillym
Actually that doesn't give me the correct answer either. In my journeys I have got:

, and now

(Headbang) - Oct 19th 2009, 01:11 PMtonio
- Oct 19th 2009, 01:12 PMbillym
Ok so the the original equation should have been:

Got it. Thanks. Goodnight.