2.1: Concept of the Derivative
The velocity of an airplane is not always consistent due to various factors, including the fact that it does not travel in a straight line. So, most people look at an average velocity to determine the speed of the plane. Sometimes, there is an instantaneous velocity used to determine the speed at a specific time. This is an example of how derivatives are used to help determine specific and average amounts.
The idea of derivatives may be challenging at first, but it makes concepts easier throughout the unit. You will start by using concepts that you know, such as slope of a line and limits. These concepts will be expanded further to help define a derivative.
Subunit 2.1 begins by defining the slope and slope of a tangent line. Then, the slope of a tangent line for a point on a graph is used to define a derivative. The derivative of a function is defined in this section, also using the concept of limits.