Answer
$C^{\prime}(1000)=\$ 4.80$ per item
Work Step by Step
The marginal cost function is the derivative $C'$ of the cost function C.
The units of marginal cost are units of cost (dollars, say) per item.
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$C(x)=10,000+5x-0.0001x^{2}$
$C^{\prime}(x)=0+5-0.0001(2x)$
$C^{\prime}(x)=5-0.0002x$
$C^{\prime}(1000)=5-0.0002(1000)$
$=5-0.2=4.8$ (dollars per item)
$C^{\prime}(1000)=\$ 4.80$ per item
