Questions from General Calculus

Q: Sales Let f (p) be the number of cars sold

Sales Let f (p) be the number of cars sold when the price is p dollars per car. Interpret the statements f (10,000) = 200,000 and f ‘(10,000) = -3.

Q: Let f (x) be the number of toys sold when

Let f (x) be the number of toys sold when x dollars are spent on advertising. Interpret the statements f (100,000) = 3,000,000 and f ‘(100,000) = 30.

Q: Let f (x) be the number (in thousands)

Let f (x) be the number (in thousands) of computers sold when the price is x hundred dollars per computer. Interpret the statements f (12) = 60 and f ‘(12) = -2. Then, estimate the number of computers...

Q: Let C(x) be the cost (in dollars)

Let C(x) be the cost (in dollars) of manufacturing x items. Interpret the statements C(2000) = 50,000 and C’(2000) = 10. Estimate the cost of manufacturing 1998 items.

Q: Let P(x) be the profit (in dollars)

Let P(x) be the profit (in dollars) from manufacturing and selling x cars. Interpret P(100) = 90,000 and P’(100) = 1200. Estimate the profit from manufacturing and selling 99 cars.

Q: Let f (x) be the value in dollars of one

Let f (x) be the value in dollars of one share of a company x days since the company went public. (a) Interpret the statements f (100) = 16 and f ‘(100) = .25. (b) Estimate the value of one share on t...

Q: Consider the cost function C(x) = 6x2 + 14x

Consider the cost function C(x) = 6x2 + 14x + 18 (thousand dollars). (a) What is the marginal cost at production level x = 5? (b) Estimate the cost of raising the production level from x = 5 to x = 5....

Q: Estimate how much the function f (x) = 1

Estimate how much the function f (x) = 1 / 1 + x2 will change if x decreases from 1 to .9.

Q: National health expenditures (in billions of dollars) from 1980 to

National health expenditures (in billions of dollars) from 1980 to 1998 are given by the function f (t) in Fig. 8. (a) How much money was spent in 1987? (b) Approximately how fast were expenditures ri...

Q: Differentiate. y = 4(x2 - 6)-3

Differentiate. y = 4(x2 - 6)-3