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The fourth derivative test

  1. May 30, 2003 #1
    I was given a remark and an example in my notes.

    Remark: If f ''(xo)=0, then fourth derivative test

    f ''(0)=0
    apply the fourth derivative test
    f(4)(x)=24 >0
    therefore (0,0) is a minimun point

    What exacly is the fourth derivative test? I can't find any resources from the internet. What if the function f(x)=x^5 ? Do we have the eighth derivative test?
  2. jcsd
  3. May 31, 2003 #2
    I don't recall there being a 4th derivative test.
  4. May 31, 2003 #3
    It looks as if you're applying the second derivative test to a second derivative.
  5. May 31, 2003 #4


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    The general idea (when the first derivative is 0) is to keep taking derivatives until you get one that's not 0. If it is an odd derivative, then you've got a horizontal inflection point. If it is an even derivative, then the sign distinguishes between max (-) and min (+).
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