BITSAT 2019 Paper

(b) Given: f(x) = 3x4+4x3−12x2 + 12
Differentiating with respect to x, we get
f (x) = 12x3+12x2 - 24x
For f (x) to be increasing
f'(x) > 0 ⇒ 12x3+12x2 - 24x > 0
12x (x ‌2 + x - 2) > 0
12x (x - 1)(x + 2) > 0
x (x -1)(x + 2 )> 0
⇒ - 2< x < 0 or x> 1

It means x ∊ (-2,0) ∪ (1, ∞).
Hence f (x) is increasing in (-2,0) and (1, ∞)