Q2. (Smoothness and Nonconvex Proximal Operators, 20pts) Consider a continuously differentiable function f: Rd - R with L-Lipschitz gradient (note f may be nonconvex) and a > 0. (a) (5pts) Prove that f(x) + 2 x3 has (1/a + L)-Lipschitz continuous gradient. (b) (5pts) Prove that f(x) + 2lx, is (1/@ - L)-strongly convex if a