If f has minimum, than
[tex]\delta f=0[/tex], [tex]\delta^2 f>0[/tex]
I think you're going to need to answer your question more clearly. I really am not sure what you're talking about.
If some function has minimum. Then variation of that function is equal zero or bigger then zero?
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.)
I mean by variation infinitesimal change of function while argument stay fiksed.
Which again makes no sense because you don't say how φ¯(x) is related to φ(x).
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