Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §3.7 Newton’s Method (and Chaos), #29 · Calculus · Applications of derivatives

If … what is

This problem is about $x^{2} + 1 = 0$ and chaos.

If $F (z) = 4 z - 4 z^{2}$ what is $F (F (z))$ ? How many solutions to $z = F (F (z))$ ? How many are not solutions to $z = F (z)$ ?

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §3.7 Newton’s Method (and Chaos), #29

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