Suppose that we're setting up a wireless data network for a small municipality. The local ISP wants to serve as many residents as possible, but greater

coverage brings greater costs. The cost $($in dollars$)$ to deploy $x$ nodes in the network is given by $C(x)=50000+205x+0\mathrm{.}014x^3$

Find the marginal cost function: $C^{\text{'}}(x)=$

It's suggested that $310$ nodes might be enough, but management needs to know what it would cost to deploy one more node in a key area. About how

much would it be$?$ $ $($round to $4$ decimal places if rounding is needed$)$

Note: You can earn partial credit on this problem.