Re: [PrimeNumbers] Primes between consecutive squares: Calculating derivatives
- 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
>> [ 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) :-)
I trust your calculations more than my own.