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Math Help - minimum value

  1. #1
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    minimum value

    Find the value of p which makes the value of p + 1/p a minimum
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  2. #2
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    Quote Originally Posted by mathaddict View Post
    Find the value of p which makes the value of p + 1/p a minimum
    I would attempt it like this:

    let  f(p) = p + \frac{1}{p}

     f'(p) = 1 - \frac{1}{p^2}

    for stationary point let  f'(p) = 0

    this implies that  \frac{1}{p^2} = 1

    so  p = \pm 1
    Last edited by U-God; October 27th 2008 at 09:36 PM.
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  3. #3
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by U-God View Post
    I would attempt it like this:

    let  f(p) = p + \frac{1}{p}

     f'(p) = 1 - \frac{1}{p^2}

    for stationary point let  f'(p) = 0

    this implies that  \frac{1}{p^2} = 1

    so  p = +/- 1
    Just a friendly suggestion.

    You can generate the plus or minus sign in LaTeX, using the command \pm. It yields \pm

    You can also generate a minus or plus sign in LaTeX, use the command \mp. It yields \mp.

    --Chris
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  4. #4
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    Quote Originally Posted by mathaddict View Post
    Find the value of p which makes the value of p + 1/p a minimum
    If p>0 then:
    p+\frac{1}{p} \geq 2\left( p \right)\left( \frac{1}{p} \right) = 2 by AM-GM.
    Now for p=1 we have a minimum.
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