 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2017/paper-1/14/a/i/solution

An interior stationary point has vanishing gradient:

\nabla f (x_{0}, y_{0}) = 0, f_{x} (x_{0}, y_{0}) = f_{y} (x_{0}, y_{0}) = 0.

For a differentiable function, this is the necessary first-order condition for an interior local minimum or local maximum.

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