Problem:
Plot the tangent line to the graph of the function

f(x) = ln(x - 6)

at the point x = 8 together with the graph of this function.

Visualization:

Using the TI-86 graphing calculator:

1. Press the GRAPH key and then pick y(x)= by pressing the F1 key.
2. If necessary, keep pressing F4 key until only y1= appears on the screen.
3. Be sure that PLOTS 1, 2 and 3 are turned-off.
4. Type in
ln(x - 6)

and press the ENTER key.

5. The WINDOW settings for the graph above is  [0, 12.6] × [-31/16, 31/16]:

Go to the WINDOW menu by pressing 2nd M2.

6. Press the MORE key so that MATH appears in the menu.
7. Press the F1 key to choose MATH.
8. Press the MORE key twice so that TANLN appears in the menu.
9. Press the F3 key to choose TANLN.
10. There is a blinking cursor on the graph; using the arrow keys move this cursor along the graph so that the x value, which is indicated at the lower left hand corner of the screen is as close to 8 as possible.
11. Press the ENTER key to draw the tangent line.
12. The TI-86 will draw the tangent line and display its slope across the bottom of the screen.

Constructed with the help of Chris O'Brien.