Maximum and minimum of function

Hello, could you help how to solve this:

Determine if there exists minimum or maximum of function http://latex.codecogs.com/gif.latex?.....x_%7Bn%7D%7D with condition http://tiny.cc/41ta1.

I know how to find out extrems (using Langrangeov function,..), but n variables somehow confuse me.

Thanks

edit

I hope I put it to right category

edit2

okay seems I'll never get answer in this forum

Re: Maximum and minimum of function

Quote:

Originally Posted by

**token22** Hello, could you help how to solve this:

Determine if there exists minimum or maximum of function

http://latex.codecogs.com/gif.latex?.....x_%7Bn%7D%7D with condition

http://tiny.cc/41ta1.

I know how to find out extrems (using Langrangeov function,..), but n variables somehow confuse me.

Thanks

edit

I hope I put it to right category

edit2

okay seems I'll never get answer in this forum

If the original post had not had those confusing commas you might have had a reply sooner.

You don't need Lagrange multipliers for this, it just needs the AM–GM inequality, which tells you straight away that the max occurs when There is no minimum, because you can get arbitrarily close to (but not equal to) zero by taking one of the x's small enough.

Re: Maximum and minimum of function

Hm, strange beacuse i used Lagrange where I used partial derivates the whole function (with n variables and so on) - Lagrange function that shoud be equal to 0 but it gave me that x_1,..x_n should be equal to zero. So I thought it has no extrems.

Edit

Yes this solution with AM-GM inequality looks good.

Thanks (I found it earlier but couldn't use it right)

Re: Maximum and minimum of function

By the way, will this solution work for just sum of x equal to c? Souldn't be condition equal to c/n ?