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One functional question.

  1. Jun 8, 2004 #1
    Hi All,

    I have a problem, and it is so confusing to me. I put it here in the hope of getting some helps to make it clear.

    Thank you,

    the problem is given below.

    What is the greatest value of b for which any real valued function f that satisfies the following properties mus also satisfy f(1)<5

    i) f is infinitively differentiable on the real numbers.
    ii)f(0)=1, f'(0)=1, f"(0)=2
    iii)|f'''(x)|<b for all x in [0,1]

    A.1
    B.2
    C.6
    D.12
    E.24
     
  2. jcsd
  3. Jun 8, 2004 #2

    matt grime

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    Science Advisor
    Homework Helper

    I would suggest looking at the Taylor series with the remainder in the form using the Mean Value Theorem, which ever one that is.
     
  4. Jun 8, 2004 #3
    Oh, It is so wonderful suggestion !!!

    So, it is solved. The correct answer is D (12)
     
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