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: