Question

For which interval the given function f(x) = 2x³ – 9x² + 12x + 7 is increasing?

Options

• `(-2, oo)`

• `(-2, 1)`

• `(-oo, -2)` or `(-1, oo)`

• `(-oo, 2)` or `(1, oo)`

Answer 1

`(-oo, 2)` or `(1, oo)`

Explanation:

f(x) = 2x³ – 9x² + 12x + 7

⇒ f'(x) = 6x² – 18x + 12

For f(x) to be increasing, f'(x) > 0

⇒ 6x² – 18x + 12 > 0

⇒ x² – 3x + 2 > 0

⇒ (x – 2)(x – 1) > 0

⇒ `x ∈ (-oo, 2)` or `(1, oo)`