Exercise 3.3.7: Prove Corollary 3.3.12: Suppose f: [a,b] R is a continuous function. Prove that the direct image ([a,b]) is a closed and bounded interval or a single number. Exercise 3.3.10: Suppose f: 10.1] → [0,1] is continuous. Show that f has a fixed point, in other words, show that there exists an x € (0.1) such that f(x) = x.