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

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- Solution 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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