Answer to Question #204564 in Calculus for zeeshan

Question #204564

a firm estimates that it can sell q units of its product with an advertising expenditure of x thousand dollars when Q=Q(x) = -X2 +600x +25 i) over whta level of advertising expenditure is the number of units of products sold is incresing ? ii) over what level of advertising expenditure is the numbers of units of product sold decreasing?


1
Expert's answer
2021-06-08T18:49:20-0400

Solution:

We are given that Q(x)=x²+600x+25Q(x)=-x² + 600x + 25 .

(i)

We need to find over what level of advertising expenditure is the number of units of product sold increasing.

Now,   Q(x)=2x+600Q'(x) = -2x+600 .

For increasing, Q'(x)>0

2x+600>0x>300x<300\Rightarrow -2x+600 > 0 \\ \Rightarrow -x>-300 \\ \Rightarrow x<300

Thus, Q(x)Q(x) is increasing for <x<300-\infty<x<300   

(ii) And decreasing for 300<x<300<x<\infty

Here is the graph of Q(x).





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Comments

abbas
12.06.21, 08:10

Thank's

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