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Math Help - Optimization Problem.

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    Optimization Problem.

    Find a positive number such that the sum of the number and its reciprocal is as small as possible.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by camherokid View Post
    Find a positive number such that the sum of the number and its reciprocal is as small as possible.
    Let the positive number be x. So we have x > 0

    we want x + 1/x to be a minimum.

    let y = x + 1/x
    => y' = 1 - 1/x^2

    for min, set y' = 0
    => 1 - 1/x^2 = 0
    => 1/x^2 = 1
    => x^2 = 1
    => x = +/- 1
    => x = 1, since x > 0

    you can check +1 and -1 using the second derivative test if you want to be sure of this, or graph x + 1/x
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