0 Problem 7. Let H - H be any norm on IR\". Let 3,3,: : (o, b) > R\" be continuous and let :3 E (ugh) be such that 3(a) a y(c}. Show that there exists some 5 :> 0 so that for all t E [c 6,: + 6} we have t) a y). [Hint Use .59 := \"1(5) 33(5) \"/2 and the continuity of 1: and y]