Learning Resources
Overview
The goal of this unit is to determine what is referred to as "instantaneous rate of change" - this idea is the foundation of differential calculus which is introduce in a later course.
Working with average rates of change initially, you will work towards finding instantaneous rate of change. You will analyze this concept through graphs, tables and written descriptions of functions. From a graph, it is possible to find how changes occur in the dependent variable for defined changes in the independent variable and how the slope of the tangent line at a point of a graph describes the instantaneous rate of change.
By studying graphs, tables and/or functional descriptions of situations, the average rate of change can be determined. As expected, for linear functions, the average rate of change will be the slope and will be constant; however, for higher power relations the average rate of change will vary in a consistent pattern. From this starting point, the meaning of instantaneous rate of change and the approximation of these rates will be developed. Using technology will help you visualize how the slope of a tangent to a curve at at point is a limit of the slopes of secant lines found by joining points nearby on the curve. This becomes the instantaneous rate at that point.
These ideas are developed by studying realistic situations that involve rates of change. The visual presentation by graphs and/or technology will be the basis of these investigations.
You should take approximately 10 hours to complete this unit.