The
points x = – 2 and  x = 3 divides the real line into
three disjoint intervals, namely, (– ∞, – 2), (– 2, 3)
and (3, ∞) Fig 6 3
Rationalised 2023-24
 MATHEMATICS
156
In the intervals (– ∞, – 2) and (3, ∞), f ′(x) is positive while in the interval (– 2, 3),
f ′(x) is negative Consequently, the function f is increasing in the intervals
(– ∞, – 2) and (3, ∞) while the function is decreasing in the interval (– 2, 3)