Mathematics: 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?

the correct answer is CStep-by-step explanation:...

SUppose the total cost C(x) to manufacture a quantity

Ответ:

ebi21

11.02.2022

Mathematics

a) C(x) is increasing in two regions: (i) $(+\infty, 8\,s)$ and (ii) $(10\,s,+\infty)$ .

b) C(x) decreases in $(8\,s, 10\,s)$ .

Step-by-step explanation:

Let $C(x) = x^{3}-27\cdot x^{2}+240\cdot x +850$ , where is the quantity of insecticide, measured in hundreds of liters, and C(x) 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 C(x) are decreasing and increasing by means of the first derivative and graphing tools. The first derivative of the function is: