Find the intervals in which the function f(x) = 3x⁴ - 4x³ - 12x² + 5 is (a) strictly increasing (b) strictly decreasing.

f(x) = 3x⁴ - 4x³ - 12x² + 5
f'(x) = 12x³ - 12x² - 24x = 12x(x² - x - 2)
f'(x) = 12x(x - 2)(x + 1)
Put f'(x) = 0 ⇒ x = 0, -1, 2
Intervals are (-∞, -1), (-1, 0), (0, 2), (2, ∞) as shown in the table.
f(x) is strictly increasing in (-1, 0)∪(2, ∞), and f(x) is strictly decreasing in (-∞, -1)∪(0, 2).