2. [10 points] (Subdifferential Computation) Consider the following function f(x) = max 0, 1 2 (x 2 1) , x R. (a) Show that f is a convex function. (b) Draw a plot of f(x) versus x. (Your plot doesn't have to be precise, as long as it serves the purpose for part (c). (c) Based on the plot, write down your conjecture for the subdifferential f(x) for all x R. (d) Prove that your conjecture in part (c) is indeed correct. (Don't forget to give the converse argument, i.e., no point outside of your characterization of subdifferential is a subgradient)