The circulation of daily English-language newspapers in the United States betwee

Question

The circulation of daily English-language newspapers in the United States between 1986 and 2000 can be modeled as
n(x) = 0.00792x3 - 0.32x2 + 3.457x + 51.588 million newspapers, where x is the number of years since 1980. 6 <= x <= 20
Use any method you want to find all relative maxima and minima of the function.
Name the relative maxima and minima and explain the method you used to find them.
Interpret the values in terms of newspaper circulation and years.


a) write the first derivative and use it to find the year when newspaper circulation was changing most rapidly.
Interpret what you found.

b) The president announces that the national deficit is increasing, but at a decreasing rate. Interpret this statement in terms of a function and its derivatives.

Explanation / Answer

n'(x) = 0.02376x2-0.64x+3.457

for finding extrema, equate n'(x) = 0

this gives x = 19.46,7.477

also, n''(x) = 0.04752x-0.64

finding value of n''(x) at

x=7.477; n''(x) < 0

x=19.46; n''(x) > 0

so,

global maximum occurs at x = 7.477

global minimum occurs at x = 19.46

(this is second order derivative test to find maxima/minima)

(a) n'(x) = 0.02376x2-0.64x+3.457

changes are maximum at x = 7.477,19.46

(b)

this means that overall national deficit is increasing but the rate at which it is growing currently is less than the rate at which it was growing in last year

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