Objectives: Now that we have defined the derivative of a function at a point, in this tutorial, we define a function which is the derivative at all points of an interval. We use the definition of a derivative to find the derivative of some functions. We also define the concepts of right-hand and left-hand derivatives and apply these concepts to piecewise defined functions. Various notations for derivative are shown. The relationship between differentiability and continuity are explored.

After working through these materials, the student should be able