Question

The function f(x) = x³ - 3x is ______.

Options

• increasing in (- ∞, - 1) ∪ (1, ∞) and decreasing in (-1, 1)

• increasing in (0, ∞) and decreasing in (- ∞, 0)

• decreasing in (0, ∞) and increasing in (- ∞, 0)

• decreasing in (- ∞, -1) u (1, ∞) and increasing in (-1, 1)

Answer 1

The function f(x) = x³ - 3x is increasing in (- ∞, - 1) ∪ (1, ∞) and decreasing in (-1, 1).

Explanation:

We have, function f(x) = x³ - 3x

⇒ f'(x) = 3x² - 3 = 3(x + 1)(x - 1)

Here, f'(x) > 0 in (- ∞, - 1) ∪ (1, ∞) and f'(x) < 0 in (-1, 1).

∴ f(x) is increasing in (- ∞, - 1) ∪ (1, ∞) and decreasing in (-1, 1).