[R] Optimization problem

[José E. Lozano]

>> How about smoothing the percentages, and then take the second 
>> derrivative to find the inflection point?
>>
>> which.max(diff(diff((lowess(percentages)$y))))
>
> This solution is what I've been using so far. The only difference is that
I am smoothing the 1st derivative, since its
> the one I want to be smooth, smoothing the percentages curve does not
produce good results.

I've noticed something:

What I am using is something like:

which.max(abs(diff(sign(diff(diff(lowess(percentages)$y))))))

"The fist value where the 2nd derivative changes its sign" To find the
f''(x)=0

But you have suggested the max value of the 2nd derivative. 

Regards,
Jose Lozano