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Homework Help: Differentiation question

  1. Jul 29, 2007 #1
    1. The problem statement, all variables and given/known data

    Show that there exists a differentiable real function:

    (f(x))^5 + f(x) + x = 0

    2. Relevant equations
    definition of the derivative: lim (as x -> a) [f(x) - f(a)]/x-a

    3. The attempt at a solution

    Not really sure where to start with this one. any help would be appreciated.
  2. jcsd
  3. Jul 30, 2007 #2


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    Science Advisor
    Homework Helper

    By (f(x))^5, did you mean the fifth power [itex]f^5(x) = (f(x))^5[/tex] or the fifth derivative [itex]f^{(5)}(x) = \frac{d^5f(x)}{dx^5}[/itex]. In the first case it's not a differential equation at all and I don't see why you need the definition for derivative.

    Please clarify what you mean exactly, and we'll give you a push in the right direction.
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