Question

The function f(x) = x² – 4x + 6 is increasing in the interval:

Options

• (0, 2)

• (–∞, 2]

• [1, 2]

• [2, ∞)

Answer 1

[2, ∞)

Explanation:

f(x) = x² – 4x + 6

f'(x) = 2x – 4

For critical points 2x – 4 = 0

⇒ x = 2

∴ Intervals (–∞, 2), (2, ∞)

Sign of f'(x) = 2x – 4

In (–∞, 2) f'(0) = − 4 < 0    ...(∴ Decreasing)

(2, ∞) f'(3) = 6 − 4 = 2 > 0    ...(∴ Increasing)

Hence, the functionf(x) is increasing in the interval [2, ∞).