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Using the Mean Value Thoerem for this Inequality?

  1. Apr 29, 2012 #1
    1. The problem statement, all variables and given/known data

    Let p > 1 and x > y > 0 Use the MVT to prove the inequality

    py^(p-1)[x-y] =< x^p - y^p =< px^(p-1)[x-y]

    3. The attempt at a solution

    The only way i only how to use the MVT is where i already have the function. Do you have to define the function from the problem? Thanks for your help.

    J
     
  2. jcsd
  3. Apr 29, 2012 #2

    LCKurtz

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    Yes, that's exactly what you have to do. Remember the MVT says$$
    f(b)-f(a) = f'(c)(b-a)$$ where ##c## is between ##a## and ##b##. Look carefully at your problem and see if you can't figure out an f(x) that might work. You need f(x) and its derivative in there. And you have x and y instead of a and b. Worry about the inequality signs after you come up with a likely f(x).
     
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