Deck 11: Derivatives Continued

Question 1

Find if ​

A)
B)
C)
D)
E)

Answer 1

Question 2

Find if ​

A)
B)
C)
D)
E)

Answer 2

Question 3

Find if ​

A)
B)
C)
D)
E)

Answer 3

Question 4

Find the derivative of the following function. ​ ​

A)
B)
C)
D)
E)

Question 5

Find the derivative of the following function. ​ ​

A)
B)
C)
D)
E)

Question 6

Find if ​

A)
B)
C)
D)
E)

Question 7

Find the derivative of the following function. ​ ​

A)
B)
C)
D)
E)

Question 8

Find the derivative of the following function. ​ ​

A)
B)
C) ​
D) ​
E) ​

Question 9

Find . ​ ​

A)
B)
C)
D)
E)

Question 10

Which of the following functions has the same derivative as the function below? ​ ​

A)
B)
C)
D)
E)

Question 11

Find the derivative of the following function. ​ ​

A)
B)
C)
D)
E)

Question 12

Find ​ ​

A)
B)
C)
D)
E)

Question 13

Find the derivative of the following function. ​ ​

A)
B)
C)
D)
E)

Question 14

Find . ​ ​

A)
B)
C)
D)
E)

Question 15

Find if ​

A)
B)
C)
D)
E)

Question 16

Find the derivative of the following function. ​ ​

A)
B)
C)
D)
E)

Question 17

Find the derivative of the following function. ​ ​

A)
B)
C)
D)
E)

Question 18

Which of the following functions has the same derivative as the function below? ​ ​

A)
B)
C)
D)
E)

Question 19

Find . ​
​ ​

A)
B)
C) ​
D)
E)

Question 20

Find if . ​

A)
B)
C) ​
D)
E)

Question 21

Find the derivative of the following function. ​ ​

A)
B)
C)
D)
E)

Question 22

Suppose that the total cost (in dollars) for a product is given by , where x is the number of units produced. Total cost functions always increase because producing more items costs more. What then must be true of the marginal cost function ? ​

A)
B)
C)
D)
E)

Question 23

The loudness of sound (L, measured in decibels) perceived by the human ear depends on intensity levels (I) according to , where is the standard threshold of audibility. If then using the change-of-base formula, we get . At what rate is the loudness changing with respect to x when the intensity is 1,000 times the standard threshold of audibility (that is, when x = 1,000)? ​

A)
B)
C)
D)
E)

Question 24

The demand function for a product is given by , where p is the price per unit in dollars when x units are demanded. Find the second derivative to see whether the rate at which the price is changing at 30 units is increasing or decreasing. ​

A) increasing
B) decreasing

Question 25

Between the years 1960 and 2002, the percent of women in the work force can be modeled by , where x is the number of years past 1950 (Source: U.S. Bureau of Labor Statistics). If this model is accurate beyond 2002, at what rate will the percent be changing in 2013? ​

A) In 2013, the rate will be changing at 0.291% per year.
B) In 2013, the rate will be changing at 0.455% per year.
C) In 2013, the rate will be changing at 0.007% per year.
D) In 2013, the rate will be changing at 1.324% per year.
E) In 2013, the rate will be changing at 0.231% per year.

Question 26

Find the y-value at the relative minima, and use a graphing utility to check your result. ​ ​

A)
B)
C)
D)
E) does not exist

Question 27

Find the derivative of the following function. ​ ​

A)
B)
C)
D)
E)

Question 28

Suppose that the total cost (in dollars) for a product is given by , where x is the number of units produced. Find the marginal cost function. ​

A)
B)
C)
D)
E)

Question 29

Find . ​ ​

A)
B)
C)
D)
E)

Question 30

Find the relative maxima, and use a graphing utility to check your results. ​Round your answer to two decimal places. ​ ​

A) ,
B) ,
C) ,
D) ,
E) does not exist

Question 31

Find . ​ ​

A)
B)
C)
D)
E)

Question 32

Suppose that the supply of x units of a product at price p dollars per unit is given by . Find the rate of change of supply price with respect to the number of units supplied. ​

A)
B)
C)
D)
E)

Question 33

Find the relative minima, and use a graphing utility to check your results. ​ ​

A) ​
B)
C)
D)
E) does not exist

Question 34

Find . ​ ​

A)
B)
C)
D)
E)

Question 35

Find the derivative of the following function. ​ ​

A)
B)
C)
D)
E)

Question 36

The pH of a solution is given by , where is the concentration of hydrogen ions (in gram atoms per liter). What is the rate of change of pH with respect to if ? Round your answer to two decimal places.

A) 0.18
B) -3.22
C) -28.95
D) 4.20
E) -66.67

Question 37

Suppose that the supply of x units of a product at price p dollars per unit is given by . Approximate the price increase associated with the number of units supplied changing from 32 to 33. Round your answer to the nearest cent. ​

A) $29.17
B) $10.61
C) $4.67
D) $7.78
E) $1.23

Question 38

Suppose that the total cost (in dollars) for a product is given by , where x is the number of units produced. Find the marginal cost when 500 units are produced, and interpret your result. Round your answer to the nearest cent. ​

A) $0.80. It will cost approximately $0.80 to make the 501st unit.
B) $0.31. It will cost approximately $0.31 to make the 501st unit.
C) $0.40. It will cost approximately $0.40 to make the 501st unit.
D) $380.95. It will cost approximately $380.95 to make the 501st unit.
E) $1.00. It will cost approximately $1.00 to make the 501st unit.

Question 39

Find . ​ ​

A)
B) ​
C)
D)
E)

Question 40

Find the derivative of the following function. ​ ​

A)
B)
C)
D)
E)

Question 41

Suppose the concentration C(t), in mg/ml, of a drug in the bloodstream t minutes after an injection is given by Find the maximum concentration and when it occurs. ​

A) Maximum concentration of 14.72 mg/ml occurs after 2.00 minutes.
B) Maximum concentration of 7.79 mg/ml occurs after 0.50 minutes.
C) Maximum concentration of 1.35 mg/ml occurs after 10.00minutes.
D) Maximum concentration of 14.46 mg/ml occurs after 2.40 minutes.
E) Maximum concentration of 13.81 mg/ml occurs after 2.80 minutes.

Question 42

Find the derivative of the following function. ​ ​

A)
B)
C)
D)
E)

Question 43

Write the equation of the line tangent to the graph of at . ​

A)
B)
C)
D)
E)

Question 44

Find any relative maxima and minima. Use a graphing utility to check your results. ​ ​

A) relative minimum at
B) relative maximum at
C) relative minimum at
D) relative maximum at
E) relative maximum at

Question 45

Find any relative maxima and minima. Use a graphing utility to check your results. ​ ​

A) relative minimum at
B) relative maximum at
C) relative minimum at
D) relative maximum at
E) relative minimum at

Question 46

Find the derivative of the following function. ​
​ ​

A)
B)
C)
D)
E)

Question 47

Find the derivative of the following function. ​ ​

A)
B)
C)
D)
E)

Question 48

Write the equation of the line tangent to the graph of at .

A)
B)
C)
D)
E) ​

Question 49

For selected years from 1978 to 2000, the number of mutual funds N, excluding money market funds, can be modeled by where t is the number of years past 1975. Find and interpret the rate of change of the number of mutual funds in 1995. Round your answer to one decimal places. ​

A) The number of mutual funds have increased from the previous year by 271.7.
B) The number of mutual funds have increased from the previous year by 444.6.
C) The number of mutual funds have increased from the previous year by 393.1.
D) The number of mutual funds have increased from the previous year by 307.3.
E) The number of mutual funds have increased from the previous year by 727.5.

Question 50

Find the derivative of the following function. ​ ​

A)
B)
C) ​
D)
E)

Question 51

Total personal income in the U.S. (in billions of dollars) for selected years from 1960 to 2002 is given in the following table. ​

​
These data can be modeled by , where x is the number of years past 1960. If this model is accurate, find the rate of change of the total U.S. personal income in 2001. Round your answer to the nearest ten million dollar.
​

A) $25.92 billion per year
B) $22.76 billion per year
C) $13.75 billion per year
D) $84.31 billion per year
E) $21.61 billion per year

Question 52

Find the derivative of the following function. ​ ​

A)
B)
C)
D)
E)

Question 53

Find the derivative of the following function. ​
​ ​

A)
B)
C)
D)
E)

Question 54

The sales decay for a product is given by , where S is the daily sales in dollars and t is the number of days since the end of a promotional campaign. Find the rate of change of sales decay. ​

A)
B)
C)
D)
E)

Question 55

Find the derivative of the following function. ​ ​

A)
B)
C)
D)
E)

Question 56

The future value that accrues when $200 is invested at 7%, compounded continuously, is , where t is the number of years. At what rate is the money in this account growing when t = 7? Round your answer to the nearest cent.

A) $1.63 per year
B) $326.46 per year
C) $15.02 per year
D) $2.15 per year
E) $22.85 per year

Question 57

Find the derivative of the following function. ​

A)
B)
C)
D)
E)

Question 58

Medical research has shown that between heartbeats, the pressure in the aorta of a normal adult is a function of time in seconds and can be modeled by the equation Use the derivative to find the rate at which the pressure is changing after 1.9 seconds. Round your answer to two decimal places. ​

A)
B)
C)
D)
E)

Question 59

Find the derivative of the following function. ​ ​

A)
B)
C)
D)
E)

Question 60

Suppose that the revenue in dollars from the sale of x units of a product is given by . Find the marginal revenue function. ​

A)
B)
C)
D)
E)

Question 61

Find dy/dx for the following equation: ​ .
​

A)
B)
C)
D)
E)

Question 62

Find dy/dx for the following equation: ​ .
​

A)
B) ​
C)
D)
E)

Question 63

Find dy/dx for the following equation: ​ .
​

A)
B)
C)
D)
E)

Question 64

If , find .

A)
B)
C)
D)
E)

Question 65

Find dy/dx for the following equation: ​ .
​

A)
B)
C)
D)
E)

Question 66

Find dy/dx at the given point without first solving for y. at ​

A)
B)
C)
D)
E)

Question 67

If , find . ​

A)
B)
C)
D)
E)

Question 68

Find dp/dq for the following equation: ​ .
​

A)
B)
C)
D)
E)

Question 69

For the given equation, find the slope of the tangent to the curve at the point . Round your answer to two decimal places. ​ ​

A) -7.10
B) 7.10
C) -1.10
D) -2.00
E) undefined

Question 70

Write the equation of the line tangent to the curve at the point .

A)
B)
C)
D)
E)

Question 71

Find dy/dx at the given point without first solving for y. at ​

A) 0
B) -180
C) 18
D) -18
E) 180

Question 72

Write the equation of the line tangent to the curve at the point . ​

A)
B)
C)
D)
E)

Question 73

If , find . ​

A)
B)
C)
D)
E)

Question 74

If find y'.

A)
B)
C)
D)
E)

Question 75

Total personal income in the U.S. (in billions of dollars) for selected years from 1960 to 2002 is given in the following table. ​

​
These data can be modeled by , where x is the number of years past 1960. Use the data to find the average rate of change from 2000 to 2002, which can be used to approximate the rate of change in 2002. Round your answer to the nearest ten million dollar.
​

A) $3.20 billion per year
B) $2.83 billion per year
C) $3.74 billion per year
D) $3.84 billion per year
E) $3.69 billion per year

Question 76

Find dy/dx for the following equation: ​ .
​

A)
B)
C)
D)
E) ​

Question 77

For the given equation, find the slope of the tangent to the curve at the point . Round your answer to two decimal places. ​ ​

A) 0.00
B) -11.06
C) 11.24
D) -85.06
E) -84.54

Question 78

Find dy/dx for the following equation: ​ ​

A)
B)
C)
D)
E)

Question 79

For the given equation, find the slope of the tangent to the curve at the point . Round your answer to two decimal places. ​ ​

A) -0.94
B) -1.06
C) -0.27
D) 0.00
E) undefined

Question 80

Find dy/dx at the given point without first solving for y. Round your answer to two decimal places. at ​

A) -0.80
B) -0.30
C) 1.45
D) 0.15
E) 0.45