Suppose that |f (x)|> 1 for all real x. Prove that f has at most one fixed point, which is a value of x such that f (x) = x, by following the procedure below.

1. Let a < b be real numbers. Explain why the Mean Value Theorem applies to f on the interval [a, b]. 2. Assume toward a contradiction that a and b are both fixed points. By using the Mean Value Theorem on the interval from part 1, find a contradiction.