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Math Help - Finding a function that works

  1. #1
    Newbie
    Joined
    May 2008
    Posts
    16

    Finding a function that works

    Hey guys, so i have the following:

    f''(a) = \lim_{h \to 0}\frac{f(a+h)-2f(a)+f(a-h)}{h^2}

    and I'm trying to figure out a function that works for that limit, but doesn't have a second derivative at a... been scratching my head over this one for a while lol thanks!
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  2. #2
    Senior Member
    Joined
    Feb 2010
    Posts
    422
    edit2: wait, no, I was right lol. Let a=0 and try x^2\sin (\frac1x).
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  3. #3
    Junior Member
    Joined
    Apr 2010
    Posts
    33
    f(a)=0

    f(x)=1 if x<a

    f(x)=-1 if x>a

    The limit clearly exists and is zero, for the numerator is identically zero. But f(x) is discontinuous at a and hence has no derivatives there.
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