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Using the Mean Value Theorem

  1. May 1, 2010 #1
    1. The problem statement, all variables and given/known data

    Use the mean value theorem to show that if x ∈ ℝ>0 then 0 < ( x + 1)^1/5 − x^1/5 < (5x^4/5)^-1

    2. Relevant equations

    MVT: f(b) = f(a) + f ' (c)*(b-a)

    3. The attempt at a solution

    I can see that (5x^(4/5))^-1 is the differential of x^1/5, but I'm not sure what to let be f(x), what to let be a, and what to let be b. Thanks.
  2. jcsd
  3. May 1, 2010 #2


    User Avatar
    Science Advisor

    Try f(x)= x^{1/5} and apply the mean value theorem to the interval [x, x+ 1] (for fixed x).
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