 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2014/paper-2/8/solution

Stationarity requires both first partial derivatives to vanish:

z_{x} = - sin x sin y = 0, z_{y} = cos x cos y = 0.

For example, choosing

x = π

and

cos y = 0

gives two points strictly inside the prescribed rectangle:

(x, y) = (π, π /2), (π, 3 π /2) .

Both satisfy the two derivative equations directly.

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