- Hi Kermit,

> f(x) = x**2/ln(x**2) = x**2/(2 ln(x))

Unless I've made a mistake, the first and second derivative

>

> I calculate the first and second derivatives of this

> approximation.

>

> [ long calculation snipped ]

>

> showing that the second derivative is negative for all x.

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) :-)

Peter - On 12/7/2010 11:34 PM, Peter Kosinar wrote:
>

Thank you.

> 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) :-)

I trust your calculations more than my own.

Kermit.