#### Answer

Marginal cost
$$
C^{\prime}(x)=1.92-0.002 x
$$
The cost of producing $100$ items is $\$ 742.08.$

#### Work Step by Step

Marginal cost
$$
C^{\prime}(x)=1.92-0.002 x
$$
The general anti-derivative of $
C^{\prime}(x)=1.92-0.002 x,
$ is
$$
C(x)=1.92 x-0.001 x^{2}+K
$$
But
$$
C(1)=1.92-0.001+K=562
$$
$\Rightarrow $
$$
K=560.081
$$
Therefore
$$
C(x)=1.92 x-0.001 x^{2}+560.081
$$
$\Rightarrow $
$$
C(100)=742.081,
$$
so the cost of producing $100$ items is $\$ 742.08.$