##### TI-Nspire For Dummies

The Tangent Line tool is a great option for exploring the instantaneous rate of change of a nonlinear function. Start with a fresh Graphs page and graph the equation f(x) = x3 – 3x2 – 2x + 6.

Here’s how it works:

1. Graph your function on the first available function on the entry line.

3. Press [MENU]→Points & Lines→Tangent to open the Tangent Line tool.

4. Click [CLICK] on the function graph, then press [CLICK] again to construct the tangent line.

5. Press [ESC] to exit the Tangent Line tool.

The second screen shows the result of these steps. You can drag the point of tangency to move the tangent line along the graph.

The third screen shows an alternative approach to this construction. Here, a line is constructed perpendicular to the x-axis. Then the point of intersection of this perpendicular line is constructed with the function. Then, the tangent to this point of intersection is constructed.

Under this scenario, you can move the tangent line by dragging the point of intersection of the x-axis and the perpendicular line. The tangent line moves along the curve more smoothly. Finally, press [MENU]Measurement to measure the slope of the tangent line.

Jeff McCalla teaches Algebra 2 and Pre-Calculus at St. Mary's Episcopal School in Memphis. He is a T3 instructor for Texas Instruments and co- founder of the TI-Nspire SuperUser group. Steve Ouellette wrote the first edition of TI-Nspire For Dummies as well as CliffsNotes® Guide to TI-Nspire.