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Decreasing function

  1. Sep 2, 2006 #1
    Now what should I look up to understand a question like this one:

    Function h is decreasing on the interval [4,infinity) and lim h(x)(with x approaching infinity)=8, what would be the limit g'(x)(with x approaching infinity)?

    I don't nessicarily need the answer, but could someone point me in the right direction?
     
  2. jcsd
  3. Sep 2, 2006 #2

    HallsofIvy

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    Earlier you asked about a function g that was simply decreasing and were told that you cannot say anything about the derivative as x went to infinity except that it would be non-negative (the limit could be 0).

    Is this a revision of that problem? If so, it is a good revision. (I won't make any remark about not being able to find g' from information about h!) The difference now is that h goes to a constant as x goes to infinity- that's more important than "decreasing". Given any [itex]\epsilon> 0[/itex], there must exist a "neighborhood of infinity" (interval [itex](a, \infty)[/itex]) on which h(x) differs less than [itex]\epsilon[/itex] from 8. What does that tell you about the derivative of h?
     
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