One of the formulas for inventory management says that the average weekly cost of ordering, paying for, and holding merchandise is
A(q) = km/q + cm + hq/2
, where q is the quantity ordered when things run low (shoes, TVs, brooms, or whatever the item might be); k is the cost of placing an order (the same, no matter how often you order); c is the cost of one item (a constant); m is the number of items sold each week (a constant); and h is the weekly holding cost per item (a constant that takes into account things such as space, utilities, insurance, and security).
Find dA/dq and d²A/dq².