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Inflection point

  1. Nov 23, 2008 #1

    I have read on this forum and on the internet that a function y(x) has an inflection point at x=c if y''(c) = 0. In other words, if we are asked to find inflection points of a function y(x), we need to solve y''(x) = 0

    My question is, don't we also need to verify if the concavity changes from c- to c+? If we have a function that has a point x=c that verify y''(c)=0, but does not change concavity from c- to c+, then I don't think ((c, y(c)) would qualify as a inflection point.

    Suppose the second derivative of some function is x2, if x=0 then the function is =0, but the function x2 is always positive, so going from 0- to 0+, there is no sign change, and thus no concavity change.

    Can somebody please clarify this concept for me?
    sorry for my bad english
  2. jcsd
  3. Nov 23, 2008 #2


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    Hello fishingspree2! :smile:

    Yes, y''(c) = 0 is a necessary condition, but not a sufficient one.

    You need another test, to make sure it hasn't "changed its mind"! :rolleyes:

    Concavity will do. :smile:
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