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Variation question

  1. Jan 23, 2012 #1
    If f has minimum, than

    [tex]\delta f=0[/tex], [tex]\delta^2 f>0[/tex]


    [tex]\delta f>0[/tex]?
  2. jcsd
  3. Jan 23, 2012 #2

    Char. Limit

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    Gold Member

    I think you're going to need to answer your question more clearly. I really am not sure what you're talking about.
  4. Jan 23, 2012 #3
    If some function has minimum. Then variation of that function is equal zero or bigger then zero?
  5. Jan 23, 2012 #4


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    Well, what do you mean by "variation" of a function? I know the "total variation of a function" on a given interval. If that is what you mean, what is the interval.

    (The derivative, if that might be what you mean, of a function, at a minimum, is 0 and the second derivative either 0 or positive. A simple example is [itex]x^2[/tex] which has a minimum at x= 0. The derivative is 2x which is 0 at x= 0 and the second derivative is 2 which is positive.)
  6. Jan 23, 2012 #5
    I mean by variation infinitesimal change of function while argument stay fiksed.



    [tex]\delta \varphi(x)=\bar{\varphi}(x)-\varphi(x)[/tex]
  7. Jan 24, 2012 #6


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    Science Advisor

    Which again makes no sense because you don't say how φ¯(x) is related to φ(x).
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