The average cost function associated with producing and marketing x units of an item is given by $AC = 2x-11+\frac{50}{x}$. Find the range of values of the output x, for which AC is increasing.

$x>5$

The correct answer is Option (2) → $x>5$

AC increases when $\frac{d}{dx}(AC)>0⇒\frac{d}{dx}\left(2x-11+\frac{50}{x}\right)>0$

$⇒2-0+50.\left(-\frac{1}{x^2}\right)>0⇒2-\frac{50}{x^2}>0$

$⇒1-\frac{25}{x^2}>0⇒X^2-25>0$

$⇒(x+5)(x-5)>0⇒x<-5$ or $x>5$

But $x$ is positive, therefore, AC increases when $x>5$.