BITSAT 2014 Paper

Let f (x) = 2x3 + 15 and g (x) = 9x2 – 12x then
f ' (x) = 6x2 for all x ∊ R
∴ f (x) is increasing function for all x ∊ R
Also , g ' (x) > 0 ⇒ 18x - 12 > 0 ⇒ x >

2

3

Thus, f (x) and g (x) both increases for x >

2

3

Let F (x) = f (x) – g (x) , F ' (x) < 0
(Since f (x) increases less rapidly than the function g (x))
⇒ 6x2 – 18x + 12 < 0 ⇒ 1 < x < 2