(a) (5 Marks) Construct a polynomial p satisfying all the following properties simultaneously (give a brief explanation): (1) p" (0) = 0. (2) p is concave down on (-co, 7]. (3) p is concave up on [7, 0o). Note: Give an explicit formula for p. (b) (5 Marks) Give an example of a function f with domain R satisfying all the following properties si- multancously (give a brief explanation): (1) f has no minimum nor maximum. (2) The supremum of f on its domain is 10. (3) The infimum of f on its domain is 0. Note: Give an explicit formula for f