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Fixed Point of a function

  1. Nov 12, 2004 #1
    Hi,
    I need to prove that f(x) has a fixed point, given that f'(x) >= 2 for all x.

    my problem is that I've reached the part in which g(x) = f(x) - x
    and g'(x) = f'(x) - 1 and therefore g'(x) >= 1
    but now i'm completely stuck. I knwo that I need to use the mean value theorem, but i just dont know where.
    thanx.
     
  2. jcsd
  3. Nov 13, 2004 #2

    Tide

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    If f '(x) >= 2 for all x then its graph would have to cross the graph of y = x at some point.
     
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