Problem 1. Let Ao be the collection of admissible functions on [a, b], i.e., A₁ = {v: [a, b] → R | v(a) = 0 = v(b)} Suppose that u Є C+1 ([a, b]). Prove that u(x) is a polynomial of degree at most n if and only if for all vЄ Ao we have .b L² dnu v'(x)dx = 0. dxn a Make sure you prove both directions of this statement.

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