Question

Given the total cost function for x units of a commodity as: $C\left(x\right)=\frac{1}{3}{x}^3+3x^2-16x+2$. Find Marginal cost function.

Answer 1

Let Marginal cost funtion be $MC\left(x\right)$

Now, $MC\left(x\right)=\frac{dC\left(x\right)}{dx}$

$\Rightarrow \frac{d(\frac{1}{3}{x}^3+3x^2-16x+2)}{dx}=x^2+6x-16$

$\therefore MC\left(x\right)=x^2+6x-16$