Find the intervals in which the following functions are strictly increasing or strictly decreasing:
f (x) = 2x³ – 9x² + 12x + 30

Let f (x) = 2x³ – 9x² + 12x + 30
∴   f '(x) = 6 x² – 18x + 12 = 6 (x² – 3x + 2) = 6 (x –1) (x – 2)
f ' (x) = 0 gives us 6 (x – 1) (x – 2) = 0 ⇒ x = 1, 2
The points x = 1, 2 divide the real line into three intervals (– ∞, 1), (1, 2), (2, ∞)
1. In the interval (– ∞, 1), f ' (x) > 0
∴   f (x) is increasing in ( – ∞, 1)
2.  In the interval (1, 2), f ' (x) < 0
∴    f(x) is decreasing in (1, 2)
3.   In the interval (2, ∞). f ' (x) > 0
∴     f (x) is increasing in (2, ∞)