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 total cost function and the marginal cost function.

$C(x)=2x^2−11x+50; MC(x)=4x−11$

The correct answer is Option (1) → $C(x)=2x^2−11x+50; MC(x)=4x−11$

$AC = 2x-11+\frac{50}{x}$

Total cost function = $TC=(AC)x$   $\left(∵AC=\frac{TC}{x}\right)$

$=\left(2x-11+\frac{50}{x}\right)x=2x^2-11x+50$

$MC=\frac{d}{dx}(TC)=\frac{d}{dx}(2x^2-11x+50)=4x-11$