# Chapter 5, Exploration 11

Move the slider to change the value of $$c$$, and observe what happens to the graph as it passes through the diagonal.

1. Identify the value of $$c$$ where the graph is tangent to the line $$y = x$$. How many fixed points are there at this value of $$c$$? What are their stabilities?
2. How many fixed points are there prior to this value of $$c$$? What are their stabilities?
3. How many fixed points are there after this value of $$c$$? What are their stabilities?
4. Make a rough sketch of the bifurcation diagram or “fixed point graph.” Remember that the parameter $$c$$ is the horizontal axis and the location of the fixed points is on the vertical axis. You may consider using color to indicate stability.

c: