This week, a factory is producing 50 units of a particular commodity, and the amount being produced is increasing at the rate of two units per week. If $C(x)$ is the total cost of producing x units, and $C(x) = 0.08x^3-x^2+10x+48$, find the current rate at which the production cost is increasing.
How I approach the problem:
$C^\prime(50) = \$510$
So the production cost is increasing at a rate of $\$510$?? That seems unreasonable; furthermore, what is to be done with "and the amount being produced is increasing at the rate of two units per week" or is that outside info, since the problem is asking for the rate of change in production at $50$ units?