The revenue (in dollars) from the sale of x car seats for infants is given by th

Question

The revenue (in dollars) from the sale of x car seats for infants is given by the following function. R(x) = 32x - 0.010x2 0 le x le 3200 Find the average change in revenue if production is changed from 1,000 car seats to 1,050 car seats. Use the four-step process to find R'(x). Find the revenue and the instantaneous rate of change of revenue at a production level of 1,000 car seats, and interpret the results. Find the average change in revenue if production is changed from 1,000 car seats to 1,050 car seats. (Round to one decimal place as needed.) R'(x) = R(1000) = R'(1000) = Interpret these results. This means that at a production level of 1,000 car seats, the revenue is R'(1000) dollars and is increasing at a rate of R( 1000) dollars per seat. This means that at a production level of 1,000 car seats, the revenue is R( 1000) dollars and is increasing at a rate of R'(1000) dollars per seat. This means that at a production level of 1,000 car seats, the revenue is R(1000) dollars and is decreasing at a rate of R'(1000) dollars per seat.

Explanation / Answer

A)

Average Change:

[R(1050) - R(1000) ]/ (1050 - 1000)

(32*1050 - 0.010 * 1050^2 - (32*1000 - 0.010*1000^2) ) / (1050 - 1000) = 11.5

B)

R'(x) = 32 - 0.020x

C)

R(1000) = 32*1000 - 0.010 * 1000^2 = 22000

D)

R'(1000) = 32 - 0.020*1000 = 12

The answer to the multiple choice part is B.

R(x) is the formula for revenue

R'(x) is the formula for change in revenue

Since R'(1000) is positive, we know that revenue is increasing.

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