Let f be defined on an interval I and suppose that f is one to one on I.

(a) Give an example to show that f may not be monotone on I.

(b) Give an example to show that f may not be monotone on any subinterval of I.

(c) Suppose that f is continuous on I. Prove that f is monotone on I.

(d) Suppose that f has the intermediate value property on I. Prove that f is monotone on I.