If the total cost function is given by $C (x) = 10 x - 7 x^{2} + 3 x^{3}$ then the marginal average cost function (MAC) is given by,

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$\begin{aligned} 10 - 7 x + 3 x^{2} \end{aligned}$

$- 14 + 18 x$

$\begin{aligned} 10 - 14 x + 9 x^{2} \end{aligned}$

$- 7 + 6 x$

answer is C.

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Detailed Solution

Given, function is,

$C (x) = 10 x - 7 x^{2} + 3 x^{3}$

Here,

$\begin{array}{l} AC = \frac{C (x)}{x} \\ AC = \frac{10 x}{x} - \frac{7 x^{2}}{x} + \frac{3 x^{3}}{x} \end{array}$

$A C = 10 - 7 x + 3 x^{2}$

Here, marginal average cost function,

$\begin{array}{l} M A C = \frac{d}{d x} (A C) \\ M A C = \frac{d}{d x} (10 - 7 x + 3 x^{2}) \\ M A C = - 7 + 6 x \end{array}$

Thus, the correct option is C.

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