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# (Average cost and marginal cost) If it costs a manufacturer $C(x)$ dollars to produce $x$ items, then his average cost of production is $C(x) / x$ dollars per item....

## Question

###### (Average cost and marginal cost) If it costs a manufacturer $C(x)$ dollars to produce $x$ items, then his average cost of production is $C(x) / x$ dollars per item. Typically the average cost is a decreasing function of $x$ for small $x$ and an increasing function of $x$ for large $x$. (Why?) Show that the value of $x$ that minimizes the average cost makes the average cost equal to the marginal cost.

(Average cost and marginal cost) If it costs a manufacturer $C(x)$ dollars to produce $x$ items, then his average cost of production is $C(x) / x$ dollars per item. Typically the average cost is a decreasing function of $x$ for small $x$ and an increasing function of $x$ for large $x$. (Why?) Show that the value of $x$ that minimizes the average cost makes the average cost equal to the marginal cost.

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