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A marine manufacturer will sell​ N(x) power boats after spending​ $x thousand on​ advertising, as given by Upper N (x )equals 970 minus StartFraction 3 comma 780 Over x EndFractionN(x)=970− 3,780 x​, 5 less than or equals x less than or equals 305≤x≤30. ​(A) Find Upper N prime (x )N′(x). ​(B) Find Upper N prime (10 )N′(10) and Upper N prime (20 )N′(20). Write a brief verbal interpretation of these results.

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Answer:

Step-by-step explanation:

[tex]N_{x}=970-\frac{3780}{x}\\\\=N^{i}_{x}=0-3780\frac{d}{dx}\frac{1}{x}\\\\=-3780(\frac{-1}{x^{2}})\\\\=\frac{3780}{x^{2}}\\\\N^{i}_{10}=\frac{3780}{100}\\\\=37.8\\\\N^{i}_{20}=\frac{3780}{400}\\\\=9.45[/tex]

There is an inverse relationship between the amount on advertisement and average number of bower boats

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