Problem:
Draw the graphs of the function

f(x) = |x2 - 1|

and its derivative on the closed interval [-2, 2].


Visualization:
Using the TI-85 graphing calculator:


[Press here to see animation again!]

  1. If you are not familiar with the graphing of functions on the TI-85, then first read the Initial Setup page from Little's Basic Guide to the TI-85.
  2. Press the GRAPH key and then pick y(x)= by pressing the F1 key.
  3. If necessary, keep pressing F4 key until only y1= appears on the screen.
  4. At the prompt y1=, type in
    abs(x^2 - 1)

    and press the ENTER key.
    You can enter abs by using the catalogue which is obtained by pressing 2nd CATALOG.

  5. At the prompt y2=, type in
    der1(y1,x,x)

    and press the ENTER key.
    You can enter der1 by pressing 2nd CALC followed by the F3 key.

  6. The range settings for the graph above is  [-2, 2] × [- 4, 4]:

  7. Press the F5 key to choose GRAPH.