2015-14 Local and absolute maximum

Find all positive integers \(n\) such that the following statement holds:

Let \(f:\mathbb{R}^n\to \mathbb {R}\) be a differentiable function that has a unique critical point \(c\). If \(f\) has a local maximum at \(c\), then \(f(c)\) is an absolute maximum of \(f\).

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2015-14 Local and absolute maximum, 4.3 out of 5 based on 7 ratings