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Find a upper bound

  1. May 16, 2009 #1
    help me, please

    if f(X) = sin(sin(x)), use a graph to find a upper bound for abs(f(4)(x))


    Thanks
     
  2. jcsd
  3. May 16, 2009 #2

    tiny-tim

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    Welcome to PF!

    Hi ZuzooVn! Welcome to PF! :smile:
    ok … draw y = sin(x).

    Now turn the paper sideways and draw x = sin(y) …

    what do you get? :wink:
     
  4. May 16, 2009 #3
    Re: Welcome to PF!

    Would u please tell me more detail about your solution????
     
  5. May 16, 2009 #4

    tiny-tim

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    Nope! o:)

    Just do it! :smile:
     
  6. May 16, 2009 #5
    Please

    Because, i didn't know how to find the upper bound
     
  7. May 16, 2009 #6

    HallsofIvy

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    tiny-tim has suggested a first step. Have you done it yet?
     
  8. May 16, 2009 #7
    yes, i have done it .

    But because i'm a Vietnamese, so my English skill isn't good :D
     
  9. May 16, 2009 #8

    HallsofIvy

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    Excellent! Thank you.

    Now, tiny-tim, what in the world are you talking about? I'm afraid I dont' see your point either.

    I would probably use "brute strength"

    If y= sin(sin(x)), then y'= -cos(sin(x))(-cos(x))= cos(x)cos(cos(x)). Now, instead of actually doing the other derivatives (because they get really messy!), use the fact that the nth derivative of (f(x)g(x)) will be [itex]\sum _nC_i f^{i}g^{n-i}[/itex] to see that we will, after three more derivatives, have a sum of 4 terms with binomial coeficients times sin and cos- and the largest possible value for sine or cosine is 1.
     
  10. May 16, 2009 #9
    Unless I made a silly mistake typing things in, it appears that Wolfram Alpha thinks it should be around 3.76.
     
  11. May 16, 2009 #10
    You need to define what f(4)(x) means. Do you mean, the fourth iteration of f on x, i.e. f o f o f o f (x)? Or do you mean (as others have interpreted) the fourth derivative of f?
     
  12. May 16, 2009 #11
    I means the fourth derivative of f
     
  13. May 16, 2009 #12

    HallsofIvy

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    Do you mean least upper bound? I get 8 as an upper bound.
     
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