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Calculus of variation

  1. Feb 26, 2014 #1
    If for some functional ##I##, ##\delta I=0## where ##\delta## is symbol for variation functional has extremum. For ##\delta^2 I>0## it is minimum, and for ##\delta^2 I<0## it is maximum. What if
    ##\delta I=\delta^2 I=0##. Then I must go with finding further variations. And if ##\delta^3I>0## is then that minimum? Or what?
     
  2. jcsd
  3. Feb 26, 2014 #2
    I suggest you ask the same question in a simpler situation: ordinary single-variable function.
     
  4. Feb 26, 2014 #3
    Use the first non-vanishing derivative. If it is an odd derivative, than you have and inflection point, otherwise it will be either a maximum or a minimum depending on its sign
     
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