how can we mathematically express a function whose the graph is a curve, like a parabola, where it has a minimum point (or maximum if opposite, it doesn't matter) BUT the minimum point is not one, but TWO points, one next to the other? is it possible?
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What do you mean by "next to"? – TonyK Oct 30 '14 at 13:24
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that they are literaly one next to the other at x axis! – trig Oct 30 '14 at 13:28
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That's impossible, I'm afraid. Given any two points, no matter how close together, there is always a point (in fact, an infinite number of points) between them. – TonyK Oct 30 '14 at 13:31
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How about $x^4-4x^2$? This has minima at $x=\sqrt{2}$ and $x=-\sqrt{2}$.
Hayden
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@trig I think you need to be a little more clear about what you mean about "next to". In $\mathbb{R}$, given $x\in \mathbb{R}$ there is no point $x^+$ such that $x<x^+$ but there is no $z$ such that $x<z<x^+$, so it isn't well-defined to say "literally one next to the other". – Hayden Oct 30 '14 at 16:01