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Math Help - Finding stationary points

  1. #1
    Senior Member
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    Finding stationary points

    The question:
    Find and identify the stationary points for y = e^{2x}(1 - x)

    My attempt:
    I differentiated the function as per here.

    But I'm not sure how to solve for x when y^{'} = e^{2x}(3 - 2x) = 0. I tried using Wolfram Alpha, but it said there are no solutions. My text states that there's a minimum point at (1/2, e/2), however.

    How can I solve this? Assistance is appreciated.
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  2. #2
    MHF Contributor
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    Quote Originally Posted by Glitch View Post
    The question:
    Find and identify the stationary points for y = e^{2x}(1 - x)

    My attempt:
    I differentiated the function as per here.

    But I'm not sure how to solve for x when y^{'} = e^{2x}(3 - 2x) = 0. I tried using Wolfram Alpha, but it said there are no solutions. My text states that there's a minimum point at (1/2, e/2), however.

    How can I solve this? Assistance is appreciated.
    dy/dx=e^(2x)(-1)+(1-x)(2)(e^(2x))=e^(2x)[1-2x]

    So when you set that to be 0, either e^(2x)=0 or 1-2x=0

    but e^(2x) cannot be 0, so the only solution is 1/2.
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  3. #3
    A Plied Mathematician
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    With your corrected derivative, and using this command, I was able to get WolframAlpha to produce the x value that solves the equation (although, really, it's quite straight-forward to solve by inspection: the exponential is never zero, and the linear multiplier term (1-2x) is zero when x = 1/2. Done.) What command did you use to try to find the root?

    [EDIT] This is the same as mathaddict's post, essentially.
    Last edited by Ackbeet; July 21st 2010 at 07:09 AM. Reason: Duplicate.
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  4. #4
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    Aha! Thanks guys!
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