Question

In which one of the following intervals is the function f(x) = x³ – 12x increasing?

Options

• (– 2, 2)

• (– ∞, – 2) ∪ (2, ∞)

• (– 2, ∞)

• (– ∞, 2)

Answer 1

(– ∞, – 2) ∪ (2, ∞)

Explanation:

Here, f(x) = x³ – 12x

f'(x) = 3x² – 12

For increasing f'(x) > 0

∴ 3x² – 12 > 0

3(x² – 4) > 0

3(x – 2)(x + 2) > 0

∴ x > 2, – 2

∴ For x = – 3

f'(– 3) = 3(– 3)² – 12

= 15 > 0

For x = 3

f'(3) = 3(3)² – 12

 = 15 > 0

∴ f(x) is increasing in interval (– ∞, – 2) ∪ (2, ∞)