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 .

d

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~coco

range =5

step-by-step explanation:

to find the range, we take the largest value and subtract the smallest value.

the largest value is 5

the smallest value is 0

the range is 5-0   =5