The cost function of a firm is given by $C(x)=\frac{x^3}{3}-4x^2-65x+70$. The value of x, that gives the minimum value of the marginal cost is :

4 units

The correct answer is Option (2) → 4 units

$C(x)=\frac{x^3}{3}-4x^2-65x+70$

$MC(x)=\frac{d}{dx}\left(\frac{x^3}{3}-4x^2-65x+70\right)$

$=x^2-8x-65$

for critical point, $\frac{dMC(x)}{dx}=0$

$\frac{d}{dx}(x^2-8x-65)=0$

$2x-8=0$

$x=4$ units