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DedPeter [7]
3 years ago
15

What is -2/3x+1/3+x=2/5? thanks.

Mathematics
1 answer:
OverLord2011 [107]3 years ago
3 0
-2/3x +1/3 +x = 2/5
⇒ 1/3x + 1/3 = 2/5
⇒ 1/3x = 2/5 -1/3
⇒ x/3 = 1/15
⇒ 15x = 3
⇒ x = 3/15
⇒ x = 1/5
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Step-by-step explanation:

For total cost function c(x), average cost is given by \frac{c(x)}{x} i.e., total cost divided by number of units produced.

Marginal average cost function refers to derivative of the average cost function i.e., \left ( \frac{c(x)}{x} \right )'

Given:c(x)=\frac{3x-2}{8x+1}

Average cost = \frac{c(x)}{x}=\frac{3x-2}{x(8x+1)}

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At x = 50 units,

\frac{c(50)}{50}=\frac{150-2}{50(400+1)}=\frac{148}{50(401)}=\frac{74}{10025}

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Average cost = \frac{c(x)}{x}=\frac{3x-2}{x(8x+1)}

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Marginal average cost:

Differentiate average cost with respect to x

Take f=3x-2\,,\,g=8x^2+x

using quotient rule, \left ( \frac{f}{g} \right )'=\frac{f'g-fg'}{g^2}

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\left ( \frac{c(x)}{x} \right )'=\left ( \frac{3x-2}{8x^2+x} \right )'\\=\left ( \frac{3(8x^2+x)-(16x+1)(3x-2)}{(8x^2+x)^2} \right )\\=\frac{24x^2+3x-48x^2-3x+32x+2}{(8x^2+x)^2}\\=\frac{-24x^2+32x-2}{(8x^2+x)^2}

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