Question

The function f(x) = 2x³ – 15x² + 36x + 6 is increasing in the interval

Options

• (–∞, 2) ∪ (3, ∞)

• (–∞, 2)

• (–∞, 2] ∪ [3, ∞)

• [3, ∞)

Answer 1

(–∞, 2] ∪ [3, ∞)

Explanation:

Given, f(x) = 2x³ – 15x² + 36x + 6

∴ f'(x) = 6x² – 30x + 36

It f'(x) ≥ 0, then f(x) is increasing.

So, 6x² – 30x + 36 ≥ 0

or x² – 5x + 6 ≥ 0

or (x – 3)(x – 2) ≥ 0

∴ x ∈ (–∞, 2] ∪ [3, ∞)