Question: Let (a, b) be an open interval of R (note: a = or b = is allowed). Let C(a, b), C1(a, b), and C(a, b)

Let (a, b) be an open interval of R (note: a = or b = is allowed). Let C(a, b), C1(a, b), and C(a, b) denote the set of all continuous, differentiable, and infinitely-differentiable functions f : (a, b) R, respectively. Show that all three sets are vector spaces over R. If/when you cite a fact from Calculus I, please list your source. Proof.

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