Suppose f: R →→ R is a monotonic function (not necessarily continuous). True or false: The restriction of f to a closed, bounded interval [a, b] attains a maximum.

2. Let f: I R be a continuous function on a bounded, closed interval I= [a, b). Show that f has a minimum on I.

Let f : R → R be such that for all x, y ∈ R, |f(x) - f(y)| ≤ (x - y)2. Prove that f is a constant function.

1. Consider the function fƒ: R → R defined by f(x) = = 2x + 1 5- 3x when x 1. A. Consider function f at the point x = 1. Is function f continuous at this point? Why or why not? B. Consider function f at a point x = C. Consider function f at a point x = a where a is less than 1. Is function f continuous at this point? Why or why not? a where a is greater than 1. Is function f continuous at this point? Why or why not?