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

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5. Find the cycle of period 2 for the function *F*(*x*) = –*x*3. Is there a 2-cycle for the function *F*(*x*) = *x*3?

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

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

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