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**ANIMAL who** x-3x(Square root of x)/(square root of x)

or

x-3x(times)sqrt of x/sqrt of x

first solved by using the quotient rule second by simplifying first

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A manufacturer produces bolts of fabric with a fixed width. The quantity *q* of this fabric (measured in yards) that is sold is a function of the selling price *p* (in dollars per yard), so we can write *q* = *f*(*p*). Then the total revenue earned with selling price *p* is *R*(*p*) = *pf*(*p*). Given *f*(18) = 8000 and *f'*(18) = -320, find *R'*(18).1

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In this exercise we estimate the rate at which the total personal income is rising in a metropolitan area. In 1999, the population of this area was 912,300, and the population was increasing at roughly 9800 per year. The average annual income was $29,001 per capita, and this average was increasing at about $1400 per year (a little above the national average of about $1225 yearly). Use the Product Rule and these figures to estimate the rate at which total personal income was rising in the area in 1999.