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Question : The total cost to produce x handcrafted wagons is C(x) = 60 + 2x - x^2 + 5x^3 : 2151565

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use the formula for instantaneous rate of change, approximating the limit by using smaller and smaller values of h, to find the instantaneous rate of change for the function at the given value.

1) Use a graphing utility to approximate the instantaneous rate of change of f(x) = x^{1/x} at x = 1.

A) 0.5745

B) 2.0000

C) 1.0000

D) 0.5000

2) Use a graphing utility to approximate the instantaneous rate of change of f(x) = x^{-lnx} at x = 4.

A) -0.3335

B) 0.1463

C) -0.2396

D) -0.1014

Solve the problem.

3) The graph shows the average cost of a barrel of crude oil for the years 1981 to 1990 in constant 1996 dollars. Find the approximate average change in price from 1981 to 1985.

Year

A) About -$37/year

B) About -$16/year

C) About -$4/year

D) About -$8/year

4) The graph shows the total sales in thousands of dollars from the distribution of x thousand catalogs. Find the average rate of change of sales with respect to the number of catalogs distributed from 10 to 50.

Number (in thousands)

A) (3/4)

B) 2

C) 1

D) (1/4)

5) Suppose that the total profit in hundreds of dollars from selling x items is given by P(x) = -x^{2} + 8x - 13. Find the marginal profit at x = 6.

A) -$1200 per item

B) -$100 per item

C) -$400 per item

D) -$200 per item

6) The total cost to produce x handcrafted wagons is C(x) = 60 + 2x - x^{2} + 5x^{3}. Find the rate of change of cost with respect to the number of wagons produced (the marginal cost) when x = 5.

A) $670 per wagon

B) $367 per wagon

C) $427 per wagon

D) $610 per wagon

7) Suppose that the revenue from selling x radios is R(x) = 80x - (x^{2}/10) dollars. Use the function R'(x) to estimate the increase in revenue that will result from increasing production from 115 radios to 116 radios per week.

A) $56.80

B) $103.00

C) $57.00

D) $68.50

8) Suppose that the dollar cost of producing x radios is C(x) = 400 + 20x - 0.2x^{2}. Find the marginal cost when 30 radios are produced.

A) $32

B) $820

C) $8

D) -$820

9) Suppose that the dollar cost of producing x radios is c(x) = 400 + 20x - 0.2x^{2}. Find the average cost per radio of producing the first 50 radios.

A) $18.00

B) $850.00

C) $500.00

D) $900.00

10) A particular strain of influenza is known to spread according to the function p(t) = (1/3)(t^{2} + t), where t is the number of days after the first appearance of the strain and p(t) is the percentage of the population that is infected. Find the instantaneous rate of change of p with respect to t at t = 4.

A) (10/3)% per day

B) (8/3)% per day

C) (20/3)% per day

D) 3% per day

11) The graph below shows the number of tuberculosis deaths in the United States from 1989 to 1998.

Year

Estimate the average rate of change in tuberculosis deaths from 1996 to 1998.

A) About -0.5 deaths per year

B) About -20 deaths per year

C) About -90 deaths per year

D) About -50 deaths per year

12) The graph shows the population in millions of bacteria t minutes after a bactericide is introduced into a culture. Find the average rate of change of population with respect to time for the time from 1 to 4 minutes.

Time (in minutes)

A) (1/3)

B) 4

C) (1/4)

D) 3

13) The number of gallons of water in a swimming pool t minutes after the pool has started to drain is Q(t) = 50(20 - x)^{2}. How fast is the water running out at the end of 10 minutes?

A) 5000 gal/min

B) 500 gal/min

C) 1000 gal/min

D) 2500 gal/min

14) The size of a population of mice after t months is P = 100(1 + 0.2t + 0.02t^{2}). Find the growth rate at t = 19 months.

A) 96 mice/month

B) 48 mice/month

C) 192 mice/month

D) 196 mice/month

15) A ball is thrown vertically upward from the ground at a velocity of 132 feet per second. Its distance from the ground after t seconds is given by s(t) = -16t^{2} + 132t. How fast is the ball moving 3 seconds after being thrown?

A) 252 ft per sec

B) 84 ft per sec

C) 27 ft per sec

D) 36 ft per sec