MathDB

4

Part of 2005 IMC

Problems(2)

IMC 2005 day 1 pb 4

Source: Peter

7/26/2005
4) find all polynom with coeffs a permutation of [1,...,n][1,...,n] and all roots rational
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IMC 2005 day 2 pb 4

Source: Peter

7/26/2005
Let f:R→Rf: \mathbb{R} \rightarrow \mathbb{R} be a three times differentiable function. Prove that there exists w∈[−1,1]w \in [-1,1] such that f′′′(w)6=f(1)2−f(−1)2−f′(0). \frac{f'''(w)}{6} = \frac{f(1)}{2}-\frac{f(-1)}{2}-f'(0).
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