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Proof involving the mean value theorem and derivatives

  1. Jan 17, 2012 #1
    1. The problem statement, all variables and given/known data

    For [itex]\mu\geq 0, s\geq 1,[/itex] prove that [itex](1+s)^{\mu}\geq 1 + s^{\mu}[/itex]



    2. Relevant equations



    3. The attempt at a solution

    I have written a proof involving the mean value theorem and derivatives, but there must be a simpler way! I think this should be done purely algebraically. Instructor insists that [itex]\mu[/itex] is an arbitrary non-negative real number, not just a rational or an integer. So to define it we need log, etc. But I believe there is a solution that does not go into this...
     
  2. jcsd
  3. Jan 17, 2012 #2
    Re: ddd

    Forgot to say, no binomial theorem allowed
     
  4. Jan 17, 2012 #3
    Re: ddd

    Whoops, meant [itex]\mu \geq 1[/itex] and [itex]s\geq 0[/itex], not the other way around. However, they are both reals.
     
  5. Jan 17, 2012 #4

    LCKurtz

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    Gold Member

    Re: ddd

    What does this question have to do with the subject "ddd" of the thread?
     
  6. Jan 17, 2012 #5
    Re: ddd

    Whoops, meant [itex]\mu \geq 1[/itex] and [itex]s\geq 0[/itex], not the other way around. However, they are both reals.
     
  7. Jan 17, 2012 #6
    Re: ddd

    I apologize, I forgot to enter a thread name that makes sense. If we can delete this one and repost it, I'd be happy to.
     
  8. Jan 17, 2012 #7

    berkeman

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    Staff: Mentor

    Re: ddd

    (I changed the thread title for you.)
     
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