The Shape of a Graph, Part I : In the earlier section we saw how to employ the derivative to finds out the absolute minimum & maximum values of a function.  Though, there is many more information regarding a graph that can be found out from the first derivative of a function.

Let's begin this section off by revisiting a familiar topic. Let's assume that we have a function, f ( x ) . The first derivative f ′ (x), is the rate of change of the function. We utilizes this idea to recognizes where a function was increasing, decreasing or not changing.

Before reviewing this idea let's first write the mathematical definition of increasing & decreasing.  We all know what the graph of an increasing/decreasing function looks as but sometimes it is fine to contain a mathematical definition as well.