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Math Help - Mean value theorem ?

  1. #1
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    Mean value theorem ?

    Help me please with this one, I think it's refers to Mean value theorem, but not sure...

    Let us, derivative of a function f(x) - is continuous and f(0)=1. Also \forall x>0: f'(x)>f(x) .

    Prove that \forall x>0: f(x)>e^{x}

    Thanks!
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  2. #2
    Senior Member Sambit's Avatar
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    Here goes some hints. Before I solve them for you, try yourself to do it first:-

    (i) Define a function g(x) = e^{-x}f(x)

    (ii) Find g'(x) and show that g(x) is an increasing function.

    (iii) From the criterion g(x)>g(0) for all x>0, get the desired result.

    Note: No use of Mean Value Theorem whatsoever.
    Last edited by Sambit; March 9th 2011 at 07:33 PM. Reason: Note added
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  3. #3
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    Great!
    Thank you, but the lecturer wanted a solution using Mean Value Theorem...
    Is there a solution?
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  4. #4
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    Thanks

    Great!
    Thank you, but the lecturer wanted a solution using Mean Value Theorem...
    Is there a solution?
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  5. #5
    Senior Member Sambit's Avatar
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    Quote Originally Posted by sinichko View Post
    Great!
    Thank you, but the lecturer wanted a solution using Mean Value Theorem...
    Is there a solution?
    I don't think so.
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