Question

On the interval $(1,3)$ the function $f(x) = 3x + \frac{2}{x}$ is

• A. Strictly decreasing
• B. Strictly increasing
• C. Decreasing in (2, 3) only
• D. Neither increasing nor decreasing

Answer 1

Answer: (B)

Strictly increasing

Answer 2

$f(x) = 3x + \frac{2}{x}$ ⇒ $f^{'}(x) = 3 - \frac{2}{x^{2}}$

Clearly $f^{'}(x) > 0$ on the interval (1, 3)

$\therefore$ $f(x)$ is strictly increasing.