SUppose the total cost C(x) to manufacture a quantity x of insecticide (in hundreds of liters) is given by C(x) = x^3-27x^2+240x+850.
a. Where is C(x) decreasing?
b. Where is C(x) increases?

a) is increasing in two regions: (i) and (ii) .

b) decreases in .

Step-by-step explanation:

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 .

step-by-step explanation:

one of the most important purposes of surface treatment is to alter surface properties according to the requirement of specific applications. for example, hydrophobic coating has been utilized on windshield and eyeglasses. gold atom monolayer on substrate has become a popular surface bioconjugation strategy.