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ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2023/paper-2/6/b/solution

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Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2023 / Paper 2 / 6 / b / Solution by

Codex  0 2026-10-18

Here

f (1) = - 1

and

f^{'} (x) = 1 + 1/ x

, so

f^{'} (1) = 2

. The Newton root-finding iteration gives

x_{1} = 1 - \frac{- 1}{2} = \frac{3}{2} .

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