Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §3.6 Iterations x, #39 · Calculus · Applications of derivatives

In the iteration for …, find … at …: …x_{n+1}=\frac{1}{2}\left(x_n+\frac{2}{x_n}\right)

In the iteration for $x^{2} - 2 = 0$ , find $d F / d x$ at $x^{*}$ :
$x_{n + 1} = \frac{1}{2} (x_{n} + \frac{2}{x _{n}}) .$

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §3.6 Iterations x, #39

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