# Curve fitting and max slope calculation

I have a dataset:

• X variable is date (from April to October)
• Y variable is vegetation biomass data

In my study area, growing season starts around April when vegetation biomass is low and peaks around at the end of August when biomass is highest, and finishes around October.

The purpose is to determine the exactly date when the vegetation biomass increased at maximum during the start of growing season. It should be in April.

First, I did the curve fitting using Sigmoid, logistic, 4 parameter method which was the best fit for this dataset. And I got a formula of sigmoid, logistic 4 parameter method.

Now, how can I calculate maximum increase date of vegetation biomass from curve fitting line to accomplish the purpose as mentioned above?

Thanks a lot.

You basically need to differentiate the sigmoid to get some bell-like curve; this is how it looks like for standard sigmoid $1/(1+e^{-t})$:
• @QuantGuy In a first approximation diff will do (if the discretisation is equal -- if not you need something like diff(y)/diff(x) or a more serious numerical method) – user88 Aug 17 '11 at 14:31