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Confusion with the Taylor's Inequality

  1. Aug 15, 2009 #1
    Taylor's Inequality states:
    if |f n+1(x)|<=M
    then
    |Rn(x)|<=M*|x-a|^(n+1)/(n+1)!
    however,
    Rn(x)=f n+1(x)*|x-a|^(n+1)/(n+1)!+....
    it seems |Rn(x)|>=M*|x-a|^(n+1)/(n+1)! when |f n+1(x)|=M

    the inequality is wrong??
     
  2. jcsd
  3. Aug 18, 2009 #2

    HallsofIvy

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    You seem to be assuming that all derivatives of f are positive which is NOT generally true.
     
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