Activity Overview
Students are introduced to how the slope of a tangent line changes as the point of tangency to a polynomial function changes. Students drag the tangent point and collect data which is automatically displayed as a scatter plot on the same graph as the original function - then fit the data to a new function (the derivative). Many different functions (progressing from quadratic to quartic) and their derivatives are examined, then a rule for finding the derivative is explored.
Before the Activity
The activity is fairly long. Teachers should carefully preview it to see how long it will take. If students are familiar with Nspire and have good understanding of slopes and functions, then the activity could be done in one class period. It would be possible to delete or skip over some of the sample functions if time is short.
During the Activity
The Nspire activity is self-contained. Notes on the calculator direct students when to change pages and what to do on each page. The worksheet is for students to record the answers to the questions they encounter on the activity and to record the equations for the functions in each problem and the equations for the derivatives as they discover them.
After the Activity
There are some follow-up questions on the worksheet. Teachers could edit or add to this section if they needed to follow up this investigation in a different way.