However,
f is neither increasing nor decreasing in R Interval
Sign of f ′(x)
Nature of function f
(– ∞, – 2)
(–) (–) > 0
f is increasing
(– 2, 3)
(–) (+) < 0
f is decreasing
(3, ∞)
(+) (+) > 0
f is increasing
Example 12 Find intervals in which the function given by f (x) = sin 3x, x ∈

0 2
, π  is
(a) increasing (b) decreasing Solution We have
f (x) = sin 3x
or
f ′(x) = 3cos 3x
Therefore, f′(x) = 0 gives cos 3x = 0 which in turn gives 
3
3
2,
2
x
π
π
=
 (as x ∈

0 2
, π
implies 
3
3
0, 2
x
π


∈ 



) So 
6
x
=π
 and 2
π