Problem 1256 (difficulty: 5/10)

True or false? If \(\displaystyle f:\R^2\to\R\) is differentiable and for all lines through \(\displaystyle a\) \(\displaystyle f\) has a local minimum at \(\displaystyle a\) along the line, then \(\displaystyle f\) has a local minimum at \(\displaystyle a\).

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