Suppose that the cost $(in$ dollars$)$ for a company $to$ produce $x$ pairs $of$ a new line $of$ jeans $is$

$C(x)=2,000+2x+0\mathrm{.}03x^2+0\mathrm{.}0002x^3.$

$(a)$ Find the marginal cost function.

$C^{\text{'}}(x)=$

$(b)$ Find $C^{\text{'}}(60).$

What does $it$ predict?

$It$ predicts the approximate cost $of$ the $60th$ pair.

$It$ predicts the tax $of$ the $60th$ pair.

$It$ predicts the approximate cost $of$ the $61st$ pair.

$It$ predicts the cost $of2,000$ pairs.

$It$ predicts the cost difference between the $60th$ and $61st$ pair.

$(c)$ Find the actual cost $of$ manufacturing the $61st$ pair $of$ jeans. $(Round$ your answer $to$ two decimal places.$)$

$