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Homework Help: Is this possible without a calculator?

  1. Jun 15, 2010 #1
    I was doing this problem about optimization and I derived it to:

    R' = (1-lnx)/x2

    (This was the right derivative by the way as the maximum on the R function was the same answer as when R' = 0)

    Anyways as R' = 0 when stationary points occur:

    0 = (1-lnx)/x2

    I was wondering whether it was possible to do that without the help of a graph/graphics calculator because of the zero there. I managed to get the correct answer which was x=2.71 but I couldn't do it manually because of the zero even when I used the null factor law (1-lnx) = 0 or 1/x2 = 0.
  2. jcsd
  3. Jun 15, 2010 #2
    2.718281828... is the base of the natural log.

    Plug ln(x) = 2.718281828 into your calculator. The answer should be close to 1.
  4. Jun 15, 2010 #3


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    Homework Helper

    1-lnx=0 or lnx = 1

    [tex]lnx = \log_e{x} = 1[/tex]

    It is true when x = e = 2.71.
  5. Jun 15, 2010 #4
    Thank you.
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