Q:

How to calculate inflection point in C# by a given function

My function always looks like this: y = beta1 / (1 + exp(beta2 + beta3 * x)). With the data it can get, it always looks like a mirror of that (it starts with high values, then decreases) 
I have the values beta1, beta2 and beta3. Now I need to calculate the point of inflection. I guess I could do it with an algorithm, but are there any functions provided by a library I could use? (Currently I cannot use Accord.NET because I still have C# 3.5 and it does only support 4.+)
update I'd be fine with a method to take the derivative ;)
Best regards

A:

What you need is second derivation, and if the function only differs in constants, you can pre-compute it somewhere, and then only fill in constants.
Here you are: wolfram
There is no standard library function that derivates for you.

