Q17 of 292 Page 549

Let I be an interval disjoint from . Prove that the function is strictly increasing on I.

Consider

We can see f’(x) <0 in [-1,1]

i.e. f(x) is decreasing in this interval.

We can see f’(x) >0 in (-∞, -1) ∪(1, ∞)

i.e. f(x) is increasing in this interval.

Show that is increasing on .

Prove that the function is increasing for all .

Show that is increasing for all , except at .

Find the intervals on which the function is

(a) strictly increasing

(b) strictly decreasing.