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Decreasing on the interval

  1. Sep 1, 2006 #1
    When a question asks along the lines of :
    "If a function (g) is decrasing on the interval {x,x).....What would the limg'(x) be (As it approaches infinity)"

    What are they looking for? and whatequation am I using? I'm not looking for too much info on how to do, but which direction should I go in? I'm not sure what topic this would lie in.
  2. jcsd
  3. Sep 2, 2006 #2


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    Homework Helper

    If g(x) is decreasing on the interval, say [tex]x\in \[ a,\infty)[/tex] then, unless you know more about the function g(x), all you can say is [tex]\lim_{x\rightarrow\infty}g^{\prime}(x)<0,[/tex] at least that I can tell.
  4. Sep 2, 2006 #3


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    Staff Emeritus
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    "decreasing on the interval {x, x)" makes no sense. In any case, it order to talk about a limit at infinity, we would have to know what happens on some unbounded interval, say [itex](a, \infty)[/itex] as benorin said. And you still can't answer the question except as he said.

    For example, if g(x)= ax, with a any negative number, then g'(x)= a for all x and so has limit a. Without more information about g, the limit could be any negative number.
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