Answer
$C^{\prime}(10,000)=\$ 6.00$ 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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$C(x)= 20,000+7x-0.00005x^{2}$
$C^{\prime}(x)=0+7-0.00005(2x)$
$C^{\prime}(x)=7-0.0001x$
$C^{\prime}(10,000)=7-0.0001(10,000)$
$=7-1=6$ (dollars per item)
$C^{\prime}(10,000)=\$ 6.00$ per item
