The marketing division of a large firm has found that it can model the sales generated by an advertising campaign as s(u) = 0.75 u + 1.3 millions of dollars when the firm invests u thousand dollars in advertising. The firm plans to invest u(x) = 2.9x2 + 54x + 100 thousand dollars each month where x is the number of months after the beginning of the advertising campaign. How quickly will the sales for this firm be changing when x = 13? (round your answer to three decimal places.)
Answers
Answer:
Answer:
The marketing division of a large firm has found that it can model the sales generated by an advertising campaign as
S(u) = 0.75
u + 1.3 millions of dollars
when the firm invests u thousand dollars in advertising. The firm plans to invest
u(x) = −2.9x2 + 54x + 100 thousand dollars
each month where x is the number of months after the beginning of the advertising campaign.
How quickly will the sales for this firm be changing when x = 13? (Round your answer to three decimal places.)
$ _____ million per month
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Expert Solution
Step 1
We have to find rate of change of sales w.r.t. x, that is ds/dx
Step 2
Differentiate both sides of the expression of S w.r.t. x.
s-0.75u+1.3
ds
d
(0.75u+1.3)
dx
dx
ds
=0.75-+0
dx
du
dx
ds
-0.75
dx
du
dx
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Step 3
Plug expression of u and...
ds
--0.75
dx
du
dx
ds
-=0.75(-2.9x2+54x+100)
dx
dx
ds
=0.75[-2.9(2x)+54+0]
dx
ds
-=0.75[-5.8x+54]
dx
ds
-4.35x+40.5
dx