The Newton Method Applet.
This applet demonstrates the Newton method, which is a rapidly converging root finding routine.

The text fields on the bottom of the window are used to
enter the function *f(x)*, a
range for x : *x min ... x max*, *# of points
*at which the function is to be displayed and an
initial guess for a root : *x initial*.
The first derivative required by the Newton method is computed
symbolically and need not be entered.

The * Plot
f* button graphs the function on the specified domain.
After viewing the graph, the user can type in the initial guess.
Alternatively, she or he can use the fact that clicking the right mouse button
anywhere on the graph area inserts the x coordinate of the point under the
mouse pointer in the *x initial * field.
The *Start* button
initiates the iterative process of solving the
equation f(x)=0 by computing the value of the function at the
*x initial *point and displaying the
result in the output area on the right.
Clicking on the *Next *button
produces an iteration
sequence of root approximations.

*Start *and *Next *will also draw the tangent
from the current
point on the graph to the x-axis, which
is displayed as a thick blue line. Due to the large convergence rate
of the method, the tangents may become invisible after
the first few iterations.

Finally, recall that the
convergence of the Newton method is guaranteed only
when the initial guess is "sufficiently" close to the actual
root.