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 Average cost function.

Answer 1

Let Average cost function be $AC\left(x\right)$

Now, $AC\left(x\right)=\frac{C\left(x\right)}{x}$

$\Rightarrow AC\left(x\right)=\frac{(\frac{1}{3}{x}^3+3x^2-16x+2)}{x}$

$=\frac{1}{3}{x}^2+3x-16+\frac{2}{x}$

$\therefore AC\left(x\right)=\frac{1}{3}{x}^2+3x-16+\frac{2}{x}$