Graphically, find the tangent line to the graph of the function

f(x) = sin(2x)

at the point x = 0.7 as the limit of secant lines.

Using MPP:

  1. At the main menu, either enter 4 or use the arrow keys to move to 4. Slopes and press
  2. At the prompt, f(x) =, type sin(2x)
  3. At the prompt, x0 = type 0.7
  4. Press to draw the graph.
  5. At this point, you will see the graph.

  6. The program chooses intially h = ?0.5 and draws the corresponding secant lines. Slopes are shown at the left of the screen. This process, with h divided by 2 each time, is repeated several times automatically. What is interesting about this program is that when the h is too small to be seen on the screen, the scale is automatically changed and the process is repeated:

  7. Eventually you will see the tangent line as a very good approximation to the function:

  8. Pressing of any key will stop the drawing and the pressing of will return you to the previous screen where you can either change the function or the intial point x0.