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.
- At the main menu, either enter 4
or use the arrow keys to move to 4. Slopes
- At the prompt, f(x) =, type sin(2x)
- At the prompt, x0 = type 0.7
- Press to draw the graph.
- At this point, you will see the graph.
- 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:
- Eventually you will see the tangent line as a very good approximation
to the function:
- 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.