Answer in Calculus for zeeshan #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?

Solution:

We are given that “Q(x)=-xu00b2 + 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+600” .

For increasing, Q'(x)>0

“Rightarrow -2x+600 > 0n\n Rightarrow -x>-300n\ Rightarrow x<300”

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

(ii) And decreasing for “300<x<infty”

Here is the graph of Q(x).