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Math Help - Maximum and minimum of function

  1. #1
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    Maximum and minimum of function

    Hello, could you help how to solve this:
    Determine if there exists minimum or maximum of function with condition .
    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
    Last edited by token22; October 9th 2011 at 04:40 AM.
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  2. #2
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    Re: Maximum and minimum of function

    Quote Originally Posted by token22 View Post
    Hello, could you help how to solve this:
    Determine if there exists minimum or maximum of function with condition .
    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 x_1 = x_2 = \ldots = x_n = c/n. 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.
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  3. #3
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    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)
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  4. #4
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    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 ?
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