Find the intervals in which the following functions are strictly increasing or strictly decreasing:
2x³ – 6x² – 48x + 17

Let f (x) = 2x³ – 6x²– 48x + 17
∴  f ' (x) = 6x² – 12x – 48 = 6 (x² – 2x – 8) = 6 (x + 2) (x – 4)
For f (x) to be increasing,
f ' (x) > 0  ⇒ 6 (x + 2) (x – 4) > 0
⇒ (x + 2) (x – 4) > 0
∴  either x < – 2 or x > 4
∴  f (x) is increasing in (– ∞, 2) ∪ (4, ∞)
For  f (x) to be decreasing,
f ' (x) < 0 ⇒ 6 (x + 2) (x – 4) = 0
⇒  (x + 2) (x – 4) < 0 ⇒ – 2 < x < 4
∴   f (x) is decreasing in (– 2, 4)