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 Post subject: Polynomials
PostPosted: Mon, 26 Jan 2009 04:36:24 UTC 
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Here is an interesting one:
Given reals a_1<a_2<\dots<a_n and b_1<b_2<\dots<b_n, does there exist a real polynomial p such that p(a_i)=b_i and p is monotone (on \mathbb{R})?

Hint: you should know Weierstrass approximation theorem before you attempt this question.


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