Math Is Fun Forum

emil

Member

Registered: 2007-01-21

Posts: 1

lagrange multiplier refresher

Hi,

I did this a few years back and realize now that I have forgotten most of it. Shame on me.

Please look over this problem and tell me what I am doing wrong or how I can get to the right solution.

The goal: finding stationary points of f(x,y,z)=x^3+y^3+z^3 under the constraints g(x,y,z)=x^2+y^2+z^2-1=0 and h(x,y,z)=x+y+z=0.

Starting (a, b are two different Lagrange multipliers):
3x^2=2ax+b
3y^2=2ay+b
3z^2=2az+b
x^2+y^2+z^2-1=0
x+y+z=0

Now the part where I get confused. I tried to solve this system of equations and failed miserably. Can anyone help me please?

Also, with this problem, shouldn't it be possible to put the two constraints together in one? Then I get one multiplier less (but still I am not getting the right result, I think.)

Any help is, as always, greatly aprreciated.

Thanks

Emil

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: lagrange multiplier refresher

Hi emil;

The maximum is

and occurs at

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.