# Solution: 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 $$f$$.

The best solution was submitted by Choi, Inhyeok (최인혁, 2015학번). Congratulations!

Here is his solution of problem 2015-14.

Alternative solutions were submitted by 이종원 (수리과학과 2014학번, +3), 김재준 (2014학번, +3), 박훈민 (수리과학과 2013학번, +3), 박성혁 (수리과학과 2014학번, +3), 오동우 (2015학번, +3), 이영민 (수리과학과 2012학번, +3), 장기정 (수리과학과 2014학번, +3), 신준형 (2015학번, +2). One incorrect solutions were received (LAL). Delayed submissions were not graded.

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