12. (a) The fixed points are the solutions of x_{n} =
_{n}*(1 - x_{n}^{2})_{n} = 0, ^{1/2}/s^{1/2}/s

(b) The slope of the tangent line is _{n}^{2})

(c) At x_{n} = 0, the slope of the tangent line is s; at
x_{n} = 1, the slope of the tangent line is -2s.

(d) The maximum occurs where the slope of the tangent line is zero, that is, at
x_{n} = 3^{-1/2}.

(e) For x_{n} = 3^{-1/2}, x_{n+1} = 2s/3^{3/2}.
Thus x_{n+1} = 1 for s = 3^{3/2}/2 and so the dynamics are
bounded between 0 and 1 for 0 <= s <= 3^{3/2}/2.

(f) The fixed point x_{n} = 0 is stable for 0 <= s <= 1. The slope of
the tangent line at x_{n} = (sqrt(s - 1))/s is 3 - 2*s, so this fixed point
is stable for |3 - 2*s| < 1. That is, for 1 < s < 2.

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