Introduction
The group of functions is one of the focus points of Calculus, and you should already be familiar with many aspects of those functions.
In our setting, these functions will play a rather minor role and we will only briefly review the main topics of that theory.
In mathematics a differentiable function of one real variable is a function whose derivative exists at each point in its domain. In other words, the graph of a differentiable function has a non-vertical tangent line at each interior point in its domain. A differentiable function is smooth (the function is locally well approximated as a linear function at each interior point) and does not contain any break, angle, or cuspo.