When considering a function we now have to tools to measure its instantaneous rate of change. This is a subject we have been studying in math classes for a long time beginning with the slope of a line. The instantaneous rate of change of a line is its slope (a constant value) but for other functions the rate of change may be a function itself. When discussing the rate of change of a function we can look at the average rate of change, or the slope of the secant line between two points, or the instantaneous rate of change of a function, or the slope of the tangent line. Consider the following Questions:

1. What mathematical tool allows us to move from the average rate of change of a function to its instantaneous rate of change?

2. What do we call a function's instantaneous rate of change?

3. What real world quantities are related to each other as a measure of instant rate of change?