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Math Help - critical value

  1. #1
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    critical value

    Hello,

    I try to define a function f :[a,a+1]-> [q,p] , with a \in \mathbb{Z}, q,p \in \mathbb{Q}, s.t. f is smooth and has a critical value in q and p.

    Can you please help me? I try it with a lot functions, like this:

    If we first assume that q< p:

     <br />
f(t)=q+\frac{1}{exp(\frac{1}{(t-a)}-1)}*(p-q) for a+1>t>a and f(t)=q for t=a

    but it doesn't work.

    Ok this function is smooth and has a critical value at q. But not in p.

    Thanks in advance!
    Last edited by Sogan; December 11th 2010 at 06:30 AM.
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