Chapter 4.8, Problem 58E

a.

To determine

To find: The values of a in the interval $0<a\le 4$ such that the function $f\left(x\right)=ax\left(1-x\right)$ has a fixed point and find the fixed point in terms of a.

b.

To determine

To find: The polynomial $g\left(x\right)=f\left(f\left(x\right)\right)$ in terms of x and a and find its degree.

c.

To determine

To graph: The polynomial $g\left(x\right)=-a^3{x}^4+2a^3{x}^3-a^3{x}^2-a^2{x}^2+a^{2}x$ for $a=2,3$ and 4 in the interval $0\le x\le 1$.

d.

To determine

To find: The number and locations of the fixed points of g for $a=2,3$ and 4 in the interval $0\le x\le 1$.