Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §3.7 Newton’s Method (and Chaos), #37 · Calculus · Applications of derivatives

… is negative at …, positive at …, and negative at the…

This problem is about competitors of Newton.

$f (x) = x^{2} - 4$ is negative at $x = 1$ , positive at $x = 2.5$ , and negative at the midpoint $x = 1.75$ . So $x^{*}$ lies in what interval? Take a second step to cut the interval in half again.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §3.7 Newton’s Method (and Chaos), #37

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