Question
Find the intervals in which the function f (x) = 2x3 – 15x2 + 36x + 1 is
(a) strictly increasing (b) strictly decreasing
Solution
Let f (x) = 2x3 – 15x2 + 36x + 1
f ' (x) = 6x2 – 30x + 36 = 6 (x2 – 5 x + 6) = 6 (x – 2) (x – 3)
(a) For f (x) to be increasing, f' (x) > 0
i.e., 6 (x – 2) (x – 3) > 0 or (x – 2) (x – 3) > 0
⇒ either x < 2 or x > 3
∴ f (x) is increasing in x < 2 or x > 3.
(b) For f (x) to be decreasing, f ' (x) < 0
i.e. 6 (x – 2) (x – 3) < 0. or (x – 2) (x – 3) < 0
⇒ 2 < x < 3
∴ f (x) is decreasing in 2 < x < 3
