Let , where is the quantity of insecticide, measured in hundreds of liters, and is the total manufacturing cost as a function of the quantity of the insecticide, measured in US dollars. A possible approach to determine which regions of are decreasing and increasing by means of the first derivative and graphing tools. The first derivative of the function is:
(1)
Please notice that regions where C(x) is increasing has , whereas when .
We notice that is increasing in two regions: (i) and (ii) . Besides, decreases in .
Q&A. Can more than one formula from a piecewise function be applied to a value in the domain? No. Each value corresponds to one equation in a piecewise formula.