The proofs of part (b) and (c) are similar It is left as an exercise to the reader Remarks
There is a more generalised theorem, which states that if f¢(x) > 0 for x in an interval
excluding the end points and f is continuous in the interval, then f is increasing Similarly,
if f¢(x) < 0 for x in an interval excluding the end points and f is continuous in the
interval, then f is decreasing