Question

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

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

Answer 1

The correct option is B

Strictly increasing

Explanation for the correct option:

Given: $f\left(x\right)=3x+\left(\frac{2}{x}\right)$

For maxima and minima of the function, we have to find $f’(x)$

Now, differentiating both sides with respect to $x$, we get

$f’\left(x\right)=3–\left(\frac{2}{x^2}\right)$

Since, $f’\left(x\right)>0$ on the interval $(1,3)$ .

Thus, $f\left(x\right)$is strictly increasing on the interval $\left(1,3\right)$

Hence, option B is correct.