Question 1

Find the derivative of the following function. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 2

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. ​

Accepted Answer

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. 
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 3

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

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 4

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

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 5

Suppose that production of a certain agricultural crop is related to the number of hours of labor x, and the number of acres of the crop y, according to   Find the rate of change of the number of hours, with respect to the number of acres. ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
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B)    
C)    
D)    
E)

Question 6

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

Accepted Answer

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B)    
C)    
D)    
E)    
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B)    
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D)    
E)

Question 7

Find   if   ​

Accepted Answer

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E)

Question 8

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

Accepted Answer

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 
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 9

Assume that x and y are differentiable functions of t. Find   given that   ,   , and   . Round your answer to two decimal places. ​   ​

Accepted Answer

A)  -4.00 
B)  2.33 
C)  -5.25 
D)  -28.00 
E)  -9.33 
A)  -4.00 
B)  2.33 
C)  -5.25 
D)  -28.00 
E)  -9.33

Question 10

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. ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 11

Find the derivative of the following function. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 12

p is in dollars and q is the number of units. Find the elasticity of the demand function   at the price p = $10. Round your answer to two decimal places. ​

Accepted Answer

A)  0.49 
B)  0.69 
C)  0.39 
D)  0.86 
E)  0.54 
A)  0.49 
B)  0.69 
C)  0.39 
D)  0.86 
E)  0.54

Question 13

Find the derivative of the following function. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 14

Find the derivative of the following function. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 15

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. ​

Accepted Answer

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. 
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 16

Find   . ​   ​

Accepted Answer

A)    
B)    ​ 
C)    
D)    
E)    
A)    
B)    ​ 
C)    
D)    
E)

Question 17

Assume that x and y are differentiable functions of t. If   find dx/dt when   ,   , and   . ​

Accepted Answer

A)    
B)    
C)  ​   
D)    
E)    
A)    
B)    
C)  ​   
D)    
E)

Question 18

Find the derivative of the following function. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 19

The resistance R of a blood vessel to the flow of blood is a function of the radius r of the blood vessel and is given by   , where k is a constant. For   find the percent rate of change of the resistance of a blood vessel in terms of the percent rate of change in the radius of the blood vessel. ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Find the derivative of the following function.

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.

Find dy/dx for the following equation: .

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

Suppose that production of a certain agricultural crop is related to the number of hours of labor x, and the number of acres of the crop y, according to Find the rate of change of the number of hours, with respect to the number of acres.

Find dp/dq for the following equation: .

Find if

Assume that x and y are differentiable functions of t. Find given that , , and . Round your answer to two decimal places.

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.

Find the derivative of the following function.

p is in dollars and q is the number of units. Find the elasticity of the demand function at the price p = $10. Round your answer to two decimal places.

Find the derivative of the following function.

Find the derivative of the following function.

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.

Find .

Assume that x and y are differentiable functions of t. If find dx/dt when , , and .

Find the derivative of the following function.

The resistance R of a blood vessel to the flow of blood is a function of the radius r of the blood vessel and is given by , where k is a constant. For find the percent rate of change of the resistance of a blood vessel in terms of the percent rate of change in the radius of the blood vessel.

Linear Equations and Functions

Quadratic and Other Special Functions

Matrices

Inequalities and Linear Programming

Exponential and Logarithmic Functions

Mathematics of Finance

Introduction to Probability

Further Topics in Probability and Data Description

Derivatives

Derivatives

Indefinite Integrals

Definite Integrals - Techniques

A: Definite Integrals - Techniques

Functions of Two or More Variables

Algebraic Concepts 2

Algebraic Concepts 3

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Algebraic Concepts 5

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Exam 11: Derivatives Continued

Find the derivative of the following function. ​ ​

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. ​

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

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

Suppose that production of a certain agricultural crop is related to the number of hours of labor x, and the number of acres of the crop y, according to Find the rate of change of the number of hours, with respect to the number of acres. ​

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

Find if ​

Assume that x and y are differentiable functions of t. Find given that , , and . Round your answer to two decimal places. ​ ​

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. ​

Find the derivative of the following function. ​ ​

p is in dollars and q is the number of units. Find the elasticity of the demand function at the price p = $10. Round your answer to two decimal places. ​

Find the derivative of the following function. ​ ​

Find the derivative of the following function. ​ ​

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. ​

Find . ​ ​

Assume that x and y are differentiable functions of t. If find dx/dt when , , and . ​

Find the derivative of the following function. ​ ​

The resistance R of a blood vessel to the flow of blood is a function of the radius r of the blood vessel and is given by , where k is a constant. For find the percent rate of change of the resistance of a blood vessel in terms of the percent rate of change in the radius of the blood vessel. ​

Linear Equations and Functions

Quadratic and Other Special Functions

Matrices

Inequalities and Linear Programming

Exponential and Logarithmic Functions

Mathematics of Finance

Introduction to Probability

Further Topics in Probability and Data Description

Derivatives

Derivatives

Indefinite Integrals

Definite Integrals - Techniques

A: Definite Integrals - Techniques

Functions of Two or More Variables

Algebraic Concepts 2

Algebraic Concepts 3

Algebraic Concepts 4

Algebraic Concepts 5

Filters

Find the derivative of the following function.

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.

Find dy/dx for the following equation: .

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

Suppose that production of a certain agricultural crop is related to the number of hours of labor x, and the number of acres of the crop y, according to Find the rate of change of the number of hours, with respect to the number of acres.

Find dp/dq for the following equation: .

Find if

Assume that x and y are differentiable functions of t. Find given that , , and . Round your answer to two decimal places.

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.

Find the derivative of the following function.

p is in dollars and q is the number of units. Find the elasticity of the demand function at the price p = $10. Round your answer to two decimal places.

Find the derivative of the following function.

Find the derivative of the following function.

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.

Find .

Assume that x and y are differentiable functions of t. If find dx/dt when , , and .

Find the derivative of the following function.

The resistance R of a blood vessel to the flow of blood is a function of the radius r of the blood vessel and is given by , where k is a constant. For find the percent rate of change of the resistance of a blood vessel in terms of the percent rate of change in the radius of the blood vessel.