The cost of inventory depends on the ordering and storage costs according to the inventory model $\displaystyle C = (\frac{Q}{x})s + (\frac{x}{2})r $. Determine the order size that will minimize the cost, assuming that sales occur at a constant rate, Q is the number of units sold per year, r is the cost of storing one unit for 1 year, s is the cost of placing an order, and x is the number of units per order.

I differentiated and got:

$\displaystyle x = \sqrt{\frac{2Qs}{r}} $

Not sure if this is right, and not sure how to verify it. I am always supposed to explain why there is a min at x = whatever, and I can't tell if the derivative is positive or negative because of all the variables...