Question

The cost function for x units of a commodity is given by $C\left(x\right)=\frac{x^3}{3}+x^2-15x+3$. Find marginal cost function.

• A. $x^2+2x-15$
• B. $x^2-2x-15$
• C. $x^2+2x+15$
• D. None of these

Answer 1

The correct option is A $x^2+2x-15$

$\Rightarrow$ We have, $C\left(x\right)=\frac{x^3}{3}+x^2-15x+3$.

$\Rightarrow$ Marginal cost = $\frac{d}{dx}\left(C\right)$

$\Rightarrow$ Marginal cost = $\frac{d}{dx}(\frac{x^3}{3}+x^2-15x+3)$

$\Rightarrow$ Marginal cost = $\frac{3\times x^2}{3}+2\times x-15$

$\therefore$ Marginal cost = $x^2+2x-15$