Let n be a positive integer and a, b be two real numbers. Determine (with argument) whether the following subsets of R[X] are subspaces: 1. {f(X) e R[X] | f'(8) = 0}, where f'(X) denotes the derivative of f(X). 2. {S(X) e R[X] | f(m)(0) + (S' F(X) - dX) = 0}, where f(")(X) denotes the n-th derivative of f(X). 3. {f(X) € R[X] | deg(f) = n}, where n is a fixed positive integer. 4. {f(X) E R[X] | f'(1) < f(4)}.

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