Question Bl: Consider the function f (:1?) |z|_ 5 15- (a) Show that f is differentiable everywhere except at :1: = 0. (b) Compute f' (:13) where the derivative exists. (c) On what domain is the function increasing? ((1) On what domain is the function decreasing? (e) What are the critical points of f? Hint: if you restrict the function to :1: Z 0, then it can be written without using any absolute values. The same observation holds if you restrict the function to :1: 5 0. Question B2: 2 Consider the function 9(22) 2 l (' |zv| 2| l) with domain [4,4]. (in) Find all of the critical points of g(:v) (b) Find all of the local maxima and mimirna of g. (c) Does 9 have any endpoint maxima or minirna? ((1) Determine all of the absolute maxirna and minirna of 9, if any exist. Note that if we restrict ourselves to any of the subdomains [4,2], [2,U], [0,2], or [2,4], then the function can be written without using absolute values