# will locally extremal continuous function be constant

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?

• See this. Jun 11 '14 at 18:21
• Thank you, David. I've seen. Jun 11 '14 at 18:32