The cost function for the manufacture of x number of goods by a company is given by :

$C(x)=2x^3-9x^2+12x+1,$ then value of x at which marginal cost is minimum is :

$\frac{3}{2}$

The correct answer is Option (3) → $\frac{3}{2}$

The Marginal Cost (MC) is,

$MC(x)=\frac{d}{dx}(2x^3-9x^2+12x+1)$

$=6x^2-18x+12$

To find critical point, $MC'(C)=0$

$⇒12C-18=0$

$⇒C=\frac{18}{12}=\frac{3}{2}$

∴ Marginal cost is minimum at $x=\frac{3}{2}$