Chapter 14.CR, Problem 25CR

For each of the following functions, do the following.

a. Find all equilibrium points $x,0\le x\le 1$.

b. Find the value of $\left|f^{\prime }\left(x\right)\right|$at all equilibrium points.

c. Use the theorem in Section $14.3$to determine the stability of all equilibrium points.

d. Find the next four values of the sequence, starting with $x_1=0.15$.

e. Repeat part d, starting with $x_1=0.4$.

f. Repeat part d, starting with $x_1=0.65$.

g. Repeat part d, starting with $x_1=0.85$.

h. Draw a cobweb diagram, starting with $x_1=0.4$and iterating four times.

i. Discuss how the results of part d through g compare with the results of part c.

$f\left(x\right)=4.2x^2\left(1-x\right)$