Question

Let f(x) = x³ + 9x² + 33x + 13, then f(x) is ______.

Options

• a decreasing function

• an increasing function

• an odd function

• an even function

Answer 1

Let f(x) = x³ + 9x² + 33x + 13, then f(x) is an increasing function.

Explanation:

f'(x) = 3x² + 18x + 33 = 3(x² + 6x + 11)

= 3[(x + 3)² + 2] ≥ 6 > 0

∴ f(x) is an increasing function.