give the working and explanation

Since f is nondecreasing, it is both QCC and QCV. However, f is discontinuous at 2, every point in (1, 2) is a local maximum, and even though f' (0) = 0, 0 is not even a local optimum. 2. (Sundamm, Chapter 7, Exercise 8) Let {f,- l E I} be a set (nite or innite) of functions from a convex set 9 g R\" to R, where each f, is convex and bounded on 9, and {f,(a:) li E I} is bounded for every x E 9. Show that the function f, dened as f (f6) == SUP Me), 7361' is a convex function on Q. What about the function 9, dened as I: ' f .5 ? 9(56) 121 f (39) Is 9 convex? Why or why not? Hint: Start by sketching the functions f and g for a few simple examples where I has only two or three elements. If you nd the sup and inf to be somewhat confusing, you can answer the questions for the case where I is nite, and replace the sup with max, and the inf with min