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Homework Help: 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


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    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


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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


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