Having only a high-school math background (~30 years ago), I'm having issues with the idea of derivative.
I understand that it's to be considered as a sort of "acceleration" of the values of a function, i.e. the rate at which such values change. Intuitively, this explains why a straight line has a derivative of
Does this mean that it's possible to calculate one value from the previous one by using the increment specified in the derivative?
For example, let's say we have a simple function, maybe
$ f(x)=x^2 $
The values of
x = 1, 2, 3, 4, 5, ... are
1, 4, 9, 16, 25, .... The increments between each value are
3, 5, 7, 9, ..., but the derivative is
2x, which means that the increments should be
2, 4, 6, 8, ... ?
I know that I'm missing something, I just can't see what.