Question

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.

Answer 1

Explanation:

`N_(x)=970-(3780)/(x)\\\\=N^(i)_(x)=0-3780(d)/(dx)(1)/(x)\\\\=-3780((-1)/(x^(2)))\\\\=(3780)/(x^(2))\\\\N^(i)_(10)=(3780)/(100)\\\\=37.8\\\\N^(i)_(20)=(3780)/(400)\\\\=9.45`

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