The average cost function of producing and marketing 'x' units is given by $AC=2 x-20+\frac{50}{x}$. Then the value of the output x, for which the total cost is increasing is:

x > 5

The correct answer is Option (4) → x > 5

$AC = 2x - 20 + \frac{50}{x}$

$\text{Total cost } TC = x \cdot AC$

$TC = x\left(2x - 20 + \frac{50}{x}\right)$

$TC = 2x^2 - 20x + 50$

$\frac{d(TC)}{dx} = 4x - 20$

$TC \text{ is increasing when } \frac{d(TC)}{dx} > 0$

$4x - 20 > 0$

$x > 5$

The total cost is increasing for $x > 5$.