4. Find all fixed points for the logistic family kx (1 – x ) with k > 0. 5. Find the cycle of…

4.           Find all fixed points for the logistic family kx(1 – x) with k > 0.

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5.           Find the cycle of period 2 for the function F(x) = –x3. Is there a 2-cycle for the function F(x) = x3?

6.           Let D(x) denote the doubling function defined on the interval 0 :: x :: 1 and given by

 

2x if 0 :: x 1/2 and 2x – 1 if 1/2 :: x :: 1.

Show that the seeds 1/3, 1/7, and  1/15  lie  on  cycles;  and  compute their periods.