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2nd Derivative Test conquered?

  1. Jun 7, 2007 #1
    Okay, I have made up this rule. I would love to call it mine, but I am sure some one is bound to have invented it by now...

    find a such that f '(a)=0
    now find the first nth derivative such that f^n(a) !=0
    Usually n=2.

    1. If n E odd - Inflexion, If n E even, keep going...
    2. If f^n(a)>0 - Minima, If f^n(a)<0 - Maxima.

    Well that is the jist of it...
    Is it valid?:cool:
  2. jcsd
  3. Jun 8, 2007 #2
    Yes, obvious, if you visualise the function from its Taylor series expansion:

    f(x) = (x-a)^n f^n(a)/n! + ...
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