find the marginal average cost function if cost and revenue are given by $c(x)=129 + 4.3x$ and $r(x)=2x…

find the marginal average cost function if cost and revenue are given by $c(x)=129 + 4.3x$ and $r(x)=2x - 0.01x^{2}$. the marginal average cost function is $overline{c}(x)=square$.

find the marginal average cost function if cost and revenue are given by $c(x)=129 + 4.3x$ and $r(x)=2x - 0.01x^{2}$. the marginal average cost function is $overline{c}(x)=square$.

Answer

Explanation:

Step1: Find the average cost function

The average cost function $\overline{C}(x)$ is given by $\overline{C}(x)=\frac{C(x)}{x}$. Given $C(x)=129 + 4.3x$, then $\overline{C}(x)=\frac{129 + 4.3x}{x}=\frac{129}{x}+4.3=129x^{- 1}+4.3$.

Step2: Differentiate the average - cost function

To find the marginal average - cost function $\overline{C}'(x)$, we differentiate $\overline{C}(x)$ with respect to $x$. Using the power rule $\frac{d}{dx}(x^n)=nx^{n - 1}$, for $y = 129x^{-1}+4.3$, we have $\overline{C}'(x)=129\times(-1)x^{-2}+0=-\frac{129}{x^{2}}$.

Answer:

$-\frac{129}{x^{2}}$