Consider the functions fx= (4x)^r(1-x)

a) For r=2, locate the fixed points of f(x) for x is greater than of equal to 0.

What is the behavior of the iteration if we begin at x=.2, x=.5, and x=.8?

b) For r=1. 5 locate the fixed points of f(x) graphically for x is greater than or equal to 0.

For two of the fixed points, the stability is obvious - why?

For the third fixed point, use the derivative criterion to determine its stability. Then run the iteration for

x not=.2

c) If x not = 6 find the first value of r is greater than or equal to 1 for which the iteration converges to a fixed point. Do this graphically by running a script file similar to chaos.m for different values of r.