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Re: [PrimeNumbers] Primes between consecutive squares: Calculating derivatives

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  • Kermit Rose
    ... Thank you. I trust your calculations more than my own. Kermit.
    Message 1 of 3 , Dec 7, 2010
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      On 12/7/2010 11:34 PM, Peter Kosinar wrote:
      >
      > Hi Kermit,
      >
      >> f(x) = x**2/ln(x**2) = x**2/(2 ln(x))
      >>
      >> I calculate the first and second derivatives of this
      >> approximation.
      >>
      >> [ long calculation snipped ]
      >>
      >> showing that the second derivative is negative for all x.
      >
      > Unless I've made a mistake, the first and second derivative look like this:
      >
      > f'(x) = x/log(x) - 1/(2*log^2(x))
      > f''(x) = 1/log(x) - (3/2)*(1/log^2(x)) + 1/log^3(x)
      >
      > Unfortunately, they're both positive for x > sqrt(e) :-)


      Thank you.

      I trust your calculations more than my own.

      Kermit.
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