Given that the total cost function for x units of a commodity is: $C(x)=\frac{x^3}{3}+ 3x^2 - 7x + 16$. Find the marginal cost (MC).

$MC(x) = x^2 + 6x – 7$

The correct answer is Option (1) → $MC(x) = x^2 + 6x – 7$

Given total cost function $C(x)=\frac{x^3}{3}+ 3x^2 - 7x + 16$

Marginal cost (MC) = $\frac{d}{dx}(C(x))=\frac{d}{dx}\left(\frac{x^3}{3}+ 3x^2 - 7x + 16\right)$

$=\frac{1}{3}.3x^2 + 3.2x-7.1$

$=x^2 + 6x – 7$