Question

Given the marginal cost function $\frac{2x}{3}+3-\frac{16}{x^2}$, find average cost function.

• A. $\frac{1}{3}{x}^2+3x-7+\frac{16}{x}$
• B. $\frac{1}{2}{x}^2+3x-7+\frac{16}{x}$
• C. $\frac{1}{4}{x}^2+3x-7+\frac{16}{x}$
• D. None of these

Answer 1

The correct option is A $\frac{1}{3}{x}^2+3x-7+\frac{16}{x}$

$\Rightarrow$ We have $MC=\frac{2x}{3}+3-\frac{16}{x^2}$

$\Rightarrow$ $Averagecost=\int \left(MC\right)dx$

$\Rightarrow$ $Averagecost=\int (\frac{2x}{3}+3-\frac{16}{x^2})dx$

$\therefore$ $Averagecost=\frac{2x^2}{2\times 3}+3x-7+\frac{16}{x}$

$\Rightarrow$ $Averagecost=\frac{1}{3}{x}^2+3x-7+\frac{16}{x}$