Using the Newton Quotient, draw the graph of the derivative of the function
f(x) = x1/3.
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
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.