(a) Given that f (x) = 3.5x(1 − x),

(i) plot the graphs of f (x), f 2(x), f 3(x), and f 4(x);

(ii) approximate the fixed points of periods one, two, three, and four, if they exist;

(iii) determine the stability of each point computed in part (ii).

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(b) Use Mathematica to approximate the fixed points of periods one, two, and three for the complex mapping zn+1 = z2n

+ 2 + 3i.

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