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Let $f:[0, 1]\rightarrow \mathbb{R}$ be continuous function. Let us suppose that each point on the segment is either local maximum or local minimum for this function. Is this function a constant?

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  • $\begingroup$ See this. $\endgroup$ Jun 11 '14 at 18:21
  • $\begingroup$ Thank you, David. I've seen. $\endgroup$
    – shma2001
    Jun 11 '14 at 18:32
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By David Mitra the answer is contained in this

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