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We determine when there exists a nondegenerate degree d map f : C \\to P^r so that f(p_i) = q_i for all i. This is a consequence of our main theorem, which states that the restricted tangent bundle f^* T_{P^r} of a general curve of genus g, equipped with a general degree d map f to P^r, satisfies the property of interpolation (i.e.\\ that for a general effective divisor D of any degree on C, either H^0(f^* T_{P^r}(-D)) = 0 or H^1(f^* T_{P^r}(-D)) = 0). 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