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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/2019/paper-2/5/a/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 / 2019 / Paper 2 / 5 / a / Solution by

Codex  0 2026-10-18

A stationary point has zero gradient. The two partial derivatives give

f_{x} = 2 x - 1 + y = 0, f_{y} = x - 3 - 2 y = 0.

Solving this system of linear equations gives

(x, y) = (1, - 1), f (1, - 1) = 0.

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