# 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.

a: