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!]

  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

    ((x + .001)^(1/3) - x^(1/3))/.001

    and press the ENTER key.

  5. The range settings for the graph above is  [-3, 3] × [- 3, 3]:

  6. Press the F5 key to choose GRAPH.
  7. 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.