 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2008/paper-1/17/a/ii/solution

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

\nabla f = (y (1 - 2 x + y), x (1 - x + 2 y))

. At the three specified points it is respectively

(0, 1/4), (1/4, - 1/4), (- 1/4, 0) .

Each vector is perpendicular to its straight boundary edge and points out of the triangle, where

f

increases from its negative interior values. The arrows in the preceding figure mark these directions.

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