Chapter 5, Exploration 13

The graph below is not a tangent bifurcation. Animate the graph by dragging the slider from left to right to increase $$c$$. Use is to answer the following questions.

1. Identify the value of the parameter $$c$$ where the graph is tangent to the line $$y=x.$$
2. 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?
3. Draw the bifurcation diagram.
4. Explain what the difference is between these graphs and the graph for exploration 11. Can you use a single mathematical computation to explain why these two animations are not tangent bifurcations?

c: