Fixed point iteration
The diagram shows how fixed point iteration can be used to find an approximate solution to the equation x = g(x). Move the point A to your chosen starting value. The spreadsheet on the right shows successive approximations to the root in column A. You can use the toolbar to zoom in or out, or move the drawing pad to look at different parts of the graph. You will need to click on the "Move" tool before moving point A.
Do all starting points result in convergence to a root? Can all the roots be found using this method? You can explore other equations by double-clicking on the definition of g(x) and redefining it. Try g(x) = (7x - 3)/x², which is a different rearrangement of the same equation. This rearrangement allows you to find the other two roots to this equation. Notice that this gives a 'cobweb' diagram rather than the 'staircase' diagram shown by the original rearrangement.