Chapter 3, Application 38

For the first two components of this Application, you were asked to draw a fixed point graph for the logistic function. That graph should have the parameter \(a\) on the horizontal axis, and the value of the associated fixed point on the vertical axis. Use one color for a line connecting the attracting fixed points, and another for a line connecting the repelling fixed points. The interactive below may be helpful in locating the fixed points for various values of \(a\).

The graph below should be used for parts 3 and 4 of the application. We have the graph of the function.

\(f_a(x) = ax(1-x) \).

Manipulate the value of \(a\) with the slider bar, and adjust the initial condition. Determine the value of \(a\) when the fixed point at \(x=0\) changes from attracting to repelling.