The following applet can be used to approximate roots of y=f(x) using Newton's Method. Simply enter the function f(x), the value a, an initial guess for a root of f(x), and 0 ≤ n ≤ 100, the number of iterations used in Newton's Method.

The value of a can be changed by simply typing a new value, such as "1.2345", "pi/2", "sqrt(5)+cos(3)", etc. You may also change this value by using the up/down arrow keys, clicking on the x-axis or dragging the corresponding point left or right. To move the center of the graph, simply drag any point to a new location. To label the x-axis in radians (i.e. multiples of pi), click on the graph and press "control-r". To switch back, simply press "control-r" again.

Here is a list of functions that can be used with this applet.