Given a function f(x) = sin (x) where r e S = {x : x /0 (radian) }. (a) Is the set S open or closed or both or neither? (Note: No steps are required.) (b) Determine f'(x) and f"(x). (c) Define a function g(x) = f(x) + 2f'(x) + f"(x), where r E S. (i) Write g(x) explicitly. (ii) Is g(r) convex over S or concave over S or both or neither? Why? (iii) Is g(r) strictly convex over S or strictly concave over S or both or neither? Why