 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2025/paper-1/16/b/solution

At the central stationary point,

u = v = 0

, so

f = 0

. At each of the other stationary points,

u^{2} + v^{2} = 2

and hence

f = uv / e

. Therefore

f (1, - 1) f (2, 0) = f (0, - 2) f (2, - 2) = f (0, 0) = 0, = e^{- 1}, = - e^{- 1} .

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