Question

The real function f(x) = 2x³ – 3x² – 36x + 7 is:

Options

• Strictly increasing in (−∞, −2) and strictly decreasing in (−2, ∞)

• Strictly decreasing in (−2, 3)

• Strictly decreasing in (−∞, 3) and strictly increasing in (3, ∞)

• Strictly decreasing in (−∞, −2) ∪ (3, ∞)

Answer 1

Strictly decreasing in (−2, 3)

Explanation:

f'(x) = 6(x² − x − 6) = 6(x − 3) (x + 2)

As f'(x) < 0 ∀ x ∈ (−2, 3)

f(x) is strictly decreasing in (−2, 3)