Spring 2021 #5. Let po(x) = 1 and p(x) = x, and let P be the subspace of the space C([0, 2]) of all continuous functions on [0, 2] spanned by po and p- (a) Find a basis for P which is orthonormal with respect to the inner product (f. g) = f f(t)g(t) dt. (b) Use the results of Part (a) to find the function f(x) = ax + b in P which makes the quantity J(f) = /2 - f(x) dx as small as possible.