I am making this research about derivatives and their history. I'd like to know why were derivatives invented in the first place, to find minima and maxima for functions by calculating tangents of the curve or to calculate rate of changes or something else ?
Also, If you can suggest some good references, that would be great.
One of my favorite references for this kind of information, not just derivatives (which you'll find on page 92/390 of the pdf), is Hairer and Wanner's Analysis by Its History. Here is a link to the reference.
Hope this helps for now and the future!