Chapter 5, Exploration 12 Continued
The animation below is not a tangent bifurcation. Animate the graph by dragging the slider from left to right to increase \(c\). Use the graph to answer the following questions.
- Identify the value of the parameter \(c\) where the graph is tangent to the line \(y=x.\)
- How many fixed points are there prior to this value of \(c\)? How many fixed points are there after this value of \(c\)? What are their stabilities?
- Draw the bifurcation diagram.
- Explain what the difference is between this graph and the graph for exploration 11. Can you use a single mathematical computation to explain why this animation is not a tangent bifurcation?