Attempt $1$: $10$ attempts remaining.

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

$C(x)=4100+3x+0\mathrm{.}01x^2+0\mathrm{.}0002x^3$

$a.$ Find the rate $of$ change $of$ the cost function.

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

$b.$ Find the rate $of$ change $atx=100.$ Round $to$ two decimal places $as$ necessary.

$C^{\text{'}}(100)=,$ dollars $\frac{?}{?}$ pair

$c.$ Find the cost $atx=100.$ Round $to$ two decimal places $as$ necessary.

$C(100)=,$ dollars