The cost function for production of a commodity is

$C(x)=352+26x-0\mathrm{.}08x^2+0\mathrm{.}0004x^3$

$($a$)$ Find $C^{\text{'}}(100).$

Interpret $C^{\text{'}}(100).$

This is the amount of time, in minutes, it takes to produce $100$ items.

This is the rate at which costs are increasing with respect to the production level when $x=100.$

This is the cost of making $100$ items.

This is the number of items that must be produced before the costs reach $100.$

This is the rate at which the production level is decreasing with respect to the cost when $x=100.$

$($b$)$ Find the actual cost of producing the $101$ st item. $($Round your answer to the nearest cent.$)$ $