Answer
$C^{\prime}(100)= \$ 99.90 $ per item
Work Step by Step
The marginal cost function is the derivative $C^{\prime}$ of the cost function C.
The units of marginal cost are units of cost (dollars, say) per item.
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$C(x)=15,000+100x-\displaystyle \frac{1000}{x}$
$C(x)=15,000+100x-1000x^{-1}$
$C^{\prime}(x)=0+100+1000(-x^{-2})$
$=100-1000x^{-2}$
$C^{\prime}(100)=100-1000(100^{-2})$
$=100-0.1=99.9 $ (dollars per item)
$C^{\prime}(100)= \$ 99.90 $ per item
