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Question involving higher derivatives

  1. Mar 3, 2013 #1
    1. The problem statement, all variables and given/known data
    Which of the following satisfy (f^k)(x) = 0 for all k >= 6?

    a) f(x) = 7x^4 + 4 + x^-1
    b) f(x) = sqrt(x)
    c) f(x) = x^(9/5)
    d) f(x) = x^3 - 2
    e) f(x) = 1 - x^6
    f) f(x) = 2x^2 + 3x^5

    2. Relevant equations

    None, but given as a problem in a chapter where the topic is higher order derivatives.


    3. The attempt at a solution

    I think the answer is e) but it's true for all k not just k>=6 and I don't know how finding the answer relates to higher order derivatives or how I'd use higher order derivatives to find the solution

    k >= 6, for x = 1 & -1

    (1-1)^k = 0
    0^k = 0, lol

    Edit: Hmmm maybe I'm reading the problem wrong? Is it asking which function is always = 0 for all x, and all k >= 6?
     
    Last edited: Mar 3, 2013
  2. jcsd
  3. Mar 3, 2013 #2

    Dick

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    Science Advisor
    Homework Helper

    You misunderstand the problem. The kth derivative is supposed to be identically zero (zero for ALL values of x, not just some). What's the 6th derivative of 1-x^6?
     
  4. Mar 3, 2013 #3

    eumyang

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    Homework Helper

    That doesn't make sense. These are supposed to be higher-order derivatives, not functions raised to an exponent. For choice (e), the 1st derivative (k = 1) is
    [itex]f'(x) = -6x^5[/itex],
    which is clearly not zero.

    The question is, for which function(s) will the sixth- and higher-order derivatives be zero?
    When is
    [itex]f^{(6)}(x) = 0, f^{(7)}(x) = 0, f^{(8)}(x) = 0[/itex]
    (and so on)?
     
  5. Mar 3, 2013 #4
    Ohhh. I thought the question was asking for f to the kth power, not the kth derivative of f

    XD

    Thanks.
     
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