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Math Help - Minimum Point

  1. #1
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    Minimum Point

    A problem I need help with.

    y = 2x^2 + 480/x


    I need to find the minimum point on that graph. Help would be greatly appreciated.
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  2. #2
    Senior Member
    Joined
    Nov 2008
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    Hi

    Quote Originally Posted by Tesphen View Post
    A problem I need help with.

    y = 2x^2 + 480/x


    I need to find the minimum point on that graph. Help would be greatly appreciated.
    First step:
    You have to find the derivative

    y' = 2*2x + (-1)480/(x^2)

    second step:

    Solve y' = 0

    4x - 480/x = 0

    4x^3 - 480 = 0

    4x^3 = 480

    x^3 = 120

    third step

    find y'' and use x = 120^(1/3) to show y''(120^(1/3)) > 0 => minimum

    hint: y'' = 960/x^3 + 4

    last step

    calculate y(120^(1/3)) = ... then you know the x-coordinate and y-coordinate of your minimum

    I get y(120^{1/3}) \approx 146
    Last edited by Rapha; May 21st 2009 at 09:35 AM.
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