The marketing division of a large firm has found that it can model the sales generated by an advertising campaign asS(u) = 0.75 u + 1.3 millions of dollarswhen the firm invests u thousand dollars in advertising. The firm plans to investu(x) = −2.9x2 + 54x + 100 thousand dollarseach 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

Question
Asked Oct 21, 2019
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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 Answer

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.

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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...

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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

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