We shall now give the following analytical definitions for a function which is
increasing or decreasing on an interval Definition 1 Let I be an interval contained in the domain of a real valued function f Then f is said to be
(i)
increasing on I if x1 < x2 in I ⇒ f (x1) < f (x2) for all x1, x2 ∈ I (ii)
decreasing on I, if x1, x2 in I ⇒ f (x1) < f (x2) for all x1, x2 ∈ I