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Critical point

  1. Nov 23, 2004 #1
    what can be said about the function f, if f is continuous on [a,b], and for some c in (a,b), f(c) is both a local maximum and a local minimum?
  2. jcsd
  3. Nov 23, 2004 #2


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    If the function isn't defined by parts on [a, b], I would say it means the function is constant on [a, b]. Because if c is a local max it means that for x near c, f(x) is smaller or equal to f(c). If additionnaly, c is a local min it means that for x near c, f(x) is greater or equal to f(c). Since for all real numbers we can only have one of the three <, > or =, it will be that f(x) = f(c) near c.

    (but I'm just a student like you so don't take this too seriously)
  4. Nov 24, 2004 #3
    thank you for the reply, I think what you said makes sense and may likely be the answer. :smile:
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