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