4. (10 points) Let f : [a, b] - R be a continuous and one-to-one function, where a f(b)

4. (10 points) Let f : [a, b] + IR be a continuous and one-to-one function, where a < b are real numbers. Use the Intermediate Value Theorem to prove by contradiction that: If f (b) < f (a), then for any c (a, b) we have f (c) > f (b).