A fixed point is stable if nearby points iterate
toward the fixed point under graphical iteration. 

Click the animation to stop. 
A fixed point is stable if at the fixed point the tangent line to the graph
lies in the region between +45° and 45°. 
That is, its slope lies between +1 and 1. 
The region between these lines is shaded in blue.
If the graph crosses the diagonal inside the
blue region (on both sides), the fixed point is stable. 
