Chapter 4, Exploration 40

Holding the mouse over the points $A$ and $B$ gives their coordinates. Either of these points can be clicked and dragged to change the graph. Begin by estimating the value of the fixed point of this function and the value of the derivative of the function at the fixed point.

• Is the fixed point of this function hyperbolic or non-hyperbolic?
• Now adjust either one of the movable points just a little bit. Does the fixed point move? Do any new fixed points appear? Is this new fixed point(s) hyperbolic or non-hyperbolic?
• Is this system structurally stable?
• Can you move $A$ and $B$ in such a way that there are multiple fixed points? Do you have to move them a little or a lot?