In search of changes–derivatives

We established the concept of functions in the previous section. With the exception of constant functions defined in the entire domain, all functions have some sort of value dynamics. That means that f(x1) is different than f(x2) for some determined values of x.

The purpose of differential calculus is to measure change. For this specific task, many mathematicians of the 17th century (Leibniz and Newton were the most prominent exponents) worked hard to find a simple model to measure and predict how a symbolically defined function changed over time.

This research guided the field to one wonderful concept—a symbolic result that, under certain conditions, tells you how much and in which direction a function changes at a certain point. This is the concept of a derivative.