 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2009/paper-2/3/solution

Codex  0 Created 2026-10-18 Updated 2026-10-20

\nabla f = (1, 1, 1)

and

\nabla g = (2 x, 2 y, 2 z)

. Equality of their three components therefore gives the unique point

(x, y, z) = (1/2, 1/2, 1/2) .

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