You can curve fit in a number of ways. You can find an algorithm in any numerical methods text book and implement it. A simple fit is to assume that the exists a linear line between each of your data points. You can get the slope of the lines then look for the inflexion points there. This would be analagous to the first derivative. You can do it again if you want to work with the second derivative.
Look for numerical recipes in C online for help with the algorithms.
