Correct Answer - Option 3 : (-∞, 2] ∪ [3, ∞)
Concept:
If f′(x) ≥ 0 at each point in an interval, then the function is said to be increasing.
Calculations:
We know that, If f′(x) ≥ 0 at each point in an interval I, then the function is said to be increasing on I.
Given , f(x) = 2x3 - 15x2 + 36x + 12
Differentiating, we get
f'(x) = 6x2 - 30x + 36
f(x) is increasing function
⇒ f'(x) ≥ 0
⇒ 6x2 - 30x + 36 ≥ 0
⇒ x2 - 5x + 6 ≥ 0
⇒ (x - 2)(x - 3) ≥ 0
Hence, x ∈ (-∞, 2] ∪ [3, ∞)
The interval in which the function f(x) = 2x3 - 15x2 + 36x + 12 is increasing in (-∞, 2] ∪ [3, ∞)
