The study of calculus should include a focus on the four key mathematical representations: algebraic, geometric, numeric, and verbal. The TI-Nspire Graphs application stands ready to take care of the geometric representation of calculus concepts. The Calculator application takes care of the algebraic piece, the Lists & Spreadsheet application takes care of the numeric piece, and the Notes application can take care of the verbal piece.

To graph the function *y* = *x*^{4} – 8*x*^{2} + 5 and its derivative on the same screen, follow these steps:

If you haven’t already done so, open a new Graphs page.

Graph

*y*=*x*^{4}– 8*x*^{2}+ 5 using the first available function on the entry line.Press [CTRL][G] to open the entry line, then press

**to open the Math template, highlight the derivative template, and press [ENTER].**See the first screen. You may want to resize the window.

Type

*x*for the first field of the derivative template, and press [TAB] to move to the second field.Type f1(

*x*) or press [VAR] to see a list of available variables, select f1 from the list, and press [X] to complete the expression f1(*x*). Press [ENTER] to graph the derivative.Move the cursor to the graph of the derivative and press [CTRL][MENU]→Attributes. Change the line style to medium and dashed to provide some visual clarity between the two graphs.

See the second and third screens. If you are using TI-Nspire CX, you may want to skip this step since each graph is a different color.

Try changing f1(*x*). The graph of f1(*x*) and its derivative updates accordingly.