Find the intervals in which the following functions are strictly increasing or decreasing:

–2x³ – 9x² – 12x + 1

It is given that function f(x) = –2x³ – 9x² – 12x + 1

⇒ f’(x) = -6x² – 18x + 12

⇒ f’(x) = -6(x² +3x + 6)

⇒ f’(x) = -6(x + 1)(x + 2)

If f’(x) = 0, then we get,

⇒ x = -1 and -2

So, the points x = -1 and x = -2 divides the real line into two disjoint intervals,

(-∞,-2), (-2,-1) and (-1,∞)

So, in interval (-∞,-2),(-1,∞)

f’(x) = -6(x + 1) (x +2) < 0

Therefore, the given function (f) is strictly decreasing for x < -2 and x>-1.

So, in interval (-2.-1)

f’(x) = -6(x + 1)(x+2) > 0

Therefore, the given function (f) is strictly increasing for -2 < x < -1.