Question

what does f(21)=30 imply?

a. when the price per computer is $3000, for every $100 price increase, the sales increase by 21,000 computers.

b. when the price per computer is $2100, for every $100 price increase, the sales decrease by 8,000 computers.

c. when the price per computer is $2100, for every $100 price increase, the sales increase by 30,000 computers.

d. 30,000 computers are sold when the price is set at $210.

what does f(21)=-8 imply?

a. when the price per computer is $2100, for every $100 price increase, the sales decrease by 8,000 computers.

b. when the price per computer is $2100, for every $1000 price increase, the sales decrease by 8,000 computers.

c. 8,000 computers are sold when the price is set at $2100.

d. 21,000 computers are sold when the price is reduced by $800.

if computers are sold for $2150 per computer, computers will be sold.

Explanation:

Step1: Understand the derivative meaning

The derivative \(f^{\prime}(x)\) represents the rate of change of the function \(f(x)\). In the context of sales \(f(x)\) (number of computers sold) and price \(x\) (price per computer), \(f^{\prime}(21)\) is the rate of change of the number of computers sold with respect to the price when the price per computer is \(x = 2100\) (since \(x\) is in hundreds of dollars, \(x = 21\) means \(21\times100=\$2100\)).

Step2: Analyze the value of \(f^{\prime}(21)=- 8\)

The negative sign in \(f^{\prime}(21)=-8\) indicates that as the price (per computer) increases, the number of computers sold (sales) decreases. The magnitude \(8\) means that for every unit increase in \(x\) (where \(x\) is in hundreds of dollars, so a \(\$100\) increase in price per computer), the number of computers sold (sales) decreases by \(8000\) (since the function \(f(x)\) gives the number of computers sold in thousands. If \(x\) is in hundreds of dollars and \(f^{\prime}(x)\) is the rate of change of \(f(x)\) (in thousands of computers) with respect to \(x\)).

Answer:

A. When the price per computer is \(\$2100\), for every \(\$100\) price increase, the sales decrease by \(8000\) computers.