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Recursive Derivatives problem

  1. Sep 26, 2004 #1
    hi, could smne pls give me an idea of how to deal with this problem?

    Suppose that f(0) = 0 and that f'(0) =1 , calculate f(f(f(x))) at point x=0
    thanks a lot, any hint at all would b helpful, as i completely clueless.
  2. jcsd
  3. Sep 26, 2004 #2
    if f(0) = 0 then f(f(0)) = f(0) = 0.. it's recursive. I am not sure why you would need f'(x) to solve nothing to do with derivatives. Are you sure you typed the question correctly?
  4. Sep 26, 2004 #3
    here it is again:
    f(0) = 0 and f'(0) = 1 calculate the derivative of f(f(f(x))) at point x=0

    that's the exact question.
    thanks for the help on the second question
    Last edited: Sep 26, 2004
  5. Sep 26, 2004 #4
    Oh I see calculate the DERIVATIVE of f(f(f(0)))

    First lets set g(x) = f(f(x))
    g'(x) is therefore f'(f(x))*f'(x)

    Derivative f(g(x)) after substitution is f'(g(x))*g'(x)

    = f'(f(f(0)))*f'(f(0))*f'(0)

    What a mouthful. If I were to venture a wild crazy guess I'd say that simplifies to 1.
  6. Sep 26, 2004 #5
    oh great! i just worked it out, it did come to 1. thanks a lot.
    can u give a further hint on the other question, i'm still a bit confused there.
    thanks again, marvellous!
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