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Math Help - positive number, sum of it and recip. small as possible

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    positive number, sum of it and recip. small as possible

    "Find a positive number such that the sum of the number and its reciprocal is as small as possible."

    ??
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  2. #2
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    Quote Originally Posted by rsanford View Post
    "Find a positive number such that the sum of the number and its reciprocal is as small as possible."

    ??
    S = x + \frac{1}{x}.

    Find the minimum using calculus:

    \frac{dS}{dx} = 1 - \frac{1}{x^2}.

    Stationary points: Solve 0 = 1 - \frac{1}{x^2} subject to the restriction x > 0.

    I get x = 1. Test nature ....

    The minimum value occurs at x = 1 and the minimum value is S = 2.
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    thank you!
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