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Homework Help: Don't undertstand what they are asking

  1. Sep 12, 2013 #1
    1. The problem statement, all variables and given/known data
    The goal of this problem is to use the Intermediate Value Theorem to prove that there exists a positive number c which is the fifth root of 2.

    Another way of expressing this is that we would like to find a positive root \,c of the continuous function f(x) = x^5 - ??? .
    Note: Fill in the box with an appropriate constant to complete the definition of the function f(x).

    2. Relevant equations

    3. The attempt at a solution
    I tried 32, 1/32, which I thought they were just asking for 2^5? But I guess not.. I understand what the intermediate value theorem is, but not in the context of what they are asking.
  2. jcsd
  3. Sep 12, 2013 #2


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    You need to have f(x) = 0 when [itex]x = 2^{1/5}[/itex], not when [itex]x = 2^5[/itex].
  4. Sep 12, 2013 #3
    The root of x^5-C is when x^5-C=0. You want to find some constant C such that the root is the fifth root of 2.
  5. Sep 12, 2013 #4
    Oh got it, 2^1/5^5 = 2 so c = 2 thanks!
  6. Sep 12, 2013 #5
    C=2, but I don't get your logic.
  7. Sep 12, 2013 #6

    Ray Vickson

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    No, you are not done! You are assuming the existence of 2^(1/5), but you cannot do that: the question is asking you to prove that such a 5th root actually exists.
  8. Sep 12, 2013 #7
    ^ Listen to Ray. You haven't used the theorem! You may want to think about, say, f(0) and f(2), and how we can use these values and the theorem to show that 2 must have a positive fifth root.
  9. Sep 12, 2013 #8


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    Science Advisor

    He wrote "2^1/5^5" but meant (2^1/5)^5.
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