Using the Newton Quotient, draw the graph of the derivative of the function

Using the TI-85 graphing calculator:

[Press here to see animation again!]

- 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.
- Press the GRAPH key and then pick
**y(x)=**by pressing the F1 key. - If necessary, keep pressing F4 key until only
**y1=**appears on the screen. - At the prompt
**y1=**, type in**((x + .001)^(1/3) - x^(1/3))/.001**and press the ENTER key.

- The range settings for the graph above is
**[-3, 3]**×**[- 3, 3]**: - Press the F5 key to choose
**GRAPH**. - In this window, this is an excellent approximation to the derivative
which is
**1/3 x**.^{- 2/3}

**Comment:** The **der1** command of the TI-85 graphing calculator will
not plot the graph of this derivative properly.