SOLUTION: A firm estimates that it can sell Q units of its product with an advertising expenditure of x thousand dollars where Q = Q(x) = - x ^ 2 + 600x + 25 i) Over what level of adv

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Question 1194085: A firm estimates that it can sell Q units of its product with an advertising expenditure of x thousand dollars where
Q = Q(x) = - x ^ 2 + 600x + 25
i) Over what level of advertising expenditure is the number of units of product sold increasing?
ii) Over what level of advertising expenditure is the number of units of product sold decreasing?
Found 2 solutions by ikleyn, Boreal:
Answer by ikleyn(52799)   (Show Source): You can put this solution on YOUR website!
.

The roots of this quadratic function are  ,

or  -0.042  and  600.042, approximately.



So, the domain of the function (the area, where it is meaningful) is this interval  [0,600.042].



The function is a downward parabola with the maximum at "  " =  = 300.



So, over the interval  [0,300)  the function is increasing;  over the interval  (300,600.042]  it is decreasing.    ANSWER

Solved.



Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
The vertex is where x=-b/2a=-600/-2 or 300
It is increasing from (0, 300) and decreasing from (300, oo), units are thousands of dollars.
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