I was wondering if there are any calculus relationships implicit in Big-O notation.
For example, an algorithm linear according to Big-O notation reduces the size of the problem by a constant amount at each step, and also involves looking at each part of the input a constant number of times. The derivative of a linear expression is a constant expression, so there is some hint of a pattern. However, I haven't been able to figure out how to generalize these facts to other Big-O classes of algorithms.
Do derivatives/antiderivatives help in matching an algorithm's Big-O description with its behavior?