Question: Let P[u] (a) Find the function u,(x) that minimizes P[u] among all C2 functions that satisfy u(0) = (1) = 0. (b) Test your answer

Let P[u]

(a) Find the function u,(x) that minimizes P[u] among all C2 functions that satisfy u(0) = (1) = 0.
(b) Test your answer by computing P[u,] and then comparing with the value of P[u] when
u(x) =
(i) x-x2
(ii) 3/2x-3/2x3
(iii) 2/3 sin Ï€ x
(iv) x2 - x4

(u-Su]dx. = [

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