[R] Inflection Points

[Martin aus Chemnitz]

Hi!

Some weeks ago I discovered R. Now, I have a somewhat complicated task 
and am not sure whether R is the right tool to solve it.

I got data of several series or measurements where I have to find the 
two inflection points. I did a linear regression (with ^2 and ^3 
arguments), the problem there was that I had to look only at a very 
narrow band of measurement in order to get the approximation right at 
the essential point. (Maybe there is a better way than lm?)

Now that I have an appromiated function, I need its inflection point, 
but I could not find any R function for that. Is there any? Or can 
anyone recommend a good (possibly free) mathematical programme?

Maybe this could be helpful: All the measurements look like this and I 
marked the points of interest.

                  ,-------
                 /
                /  <--
               /
         ,----´
        /
       |  <--
       /
-----´


Thank you very much for your help

Martin