title: How to calculate inflection point in C# by a given function
body: <p>My function always looks like this: <code>y = beta1 / (1 + exp(beta2 + beta3 * x))</code>. With the data it can get, it always looks like a mirror of that (it starts with high values, then decreases) <img src="https://i.stack.imgur.com/0P8zn.jpg" alt="enter image description here">
  I have the values beta1, beta2 and beta3. Now I need to calculate <strong>the point of inflection</strong>. 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.+)</p>
  
  <p><strong>update</strong> I'd be fine with a method to take the derivative ;)</p>
  
  <p>Best regards</p>