13. (a) The fixed points are the solutions of xn =
(b) The slope of the tangent line is
(c) At xn = 0, the slope of the tangent line is 0; at xn = 1, the slope of the tangent line is -s.
(d) The maximum occurs where the slope of the tangent line is zero, that is, at xn = 2/3.
(e) For xn = 2/3, xn+1 = 4*s/27. Thus xn+1 = 1 for s = 27/4 and so the dynamics are bounded between 0 and 1 for 0 <= s <= 27/4.
(f) The fixed point xn = 0 is stable for all s. The slope of
the tangent line at xn =
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