Question 1

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

Accepted Answer

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

Question 2

Find   if   ​

Accepted Answer

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

Question 3

If   , find   . ​

Accepted Answer

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

Question 4

Suppose the weekly demand function for a product is   where p is the price in thousands of dollars and q is the number of units demanded. What is the elasticity of demand when the price is $1,000 and the quantity demanded is 714? Round your answer to two decimal places. ​

Accepted Answer

A)  η​ ≈ 14.80 
B)  η​ ≈ 7.40 
C)  η​ ≈ 16.80 
D)  η​ ≈ 14.97 
E)  η​ ≈ 124.15 
A)  η​ ≈ 14.80 
B)  η​ ≈ 7.40 
C)  η​ ≈ 16.80 
D)  η​ ≈ 14.97 
E)  η​ ≈ 124.15

Question 5

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)? ​

Accepted Answer

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

Question 6

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

Accepted Answer

A)  4.53 
B)  0.22 
C)  -0.22 
D)  1.00 
E)  -1.00 
A)  4.53 
B)  0.22 
C)  -0.22 
D)  1.00 
E)  -1.00

Question 7

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

Accepted Answer

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

Question 8

At what y-value does the curve defined by   have a vertical tangent? ​

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

Find the derivative of the following function. ​   ​

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

Find   implicitly for

Accepted Answer

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

Question 13

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

Accepted Answer

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

Question 14

Assume that s, r, and h are differentiable functions of t. If   , find   when   ,   ,   , and   . Round your answer to two decimal places. ​

Accepted Answer

A)  0.05 
B)  1.50 
C)  0.07 
D)  2.06 
E)  0.77 
A)  0.05 
B)  1.50 
C)  0.07 
D)  2.06 
E)  0.77

Question 15

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

Accepted Answer

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

Question 16

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

Accepted Answer

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

Question 17

Find the derivative of the following function. ​

Accepted Answer

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

Question 18

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. ​

Accepted Answer

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

Question 19

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

Accepted Answer

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

Question 20

Assume that x and y are differentiable functions of t. A point is moving along the graph of the equation   At what rate is y changing when   and is changing at a rate of 4 units/sec? ​

Accepted Answer

A)  96 units/sec 
B)  92 units/sec 
C)  87 units/sec 
D)  60 units/sec 
E)  44 units/sec 
A)  96 units/sec 
B)  92 units/sec 
C)  87 units/sec 
D)  60 units/sec 
E)  44 units/sec

Find dy/dx for the following equation: .

Find if

If , find .

Suppose the weekly demand function for a product is where p is the price in thousands of dollars and q is the number of units demanded. What is the elasticity of demand when the price is $1,000 and the quantity demanded is 714? Round your answer to two decimal places.

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

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

At what y-value does the curve defined by have a vertical tangent?

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

Find the derivative of the following function.

Find the derivative of the following function.

Find implicitly for

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

Assume that s, r, and h are differentiable functions of t. If , find when , , , and . Round your answer to two decimal places.

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

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

Find the derivative of the following function.

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.

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

Assume that x and y are differentiable functions of t. A point is moving along the graph of the equation At what rate is y changing when and is changing at a rate of 4 units/sec?

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

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Exam 11: Derivatives Continued

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

Find if ​

If , find . ​

Suppose the weekly demand function for a product is where p is the price in thousands of dollars and q is the number of units demanded. What is the elasticity of demand when the price is $1,000 and the quantity demanded is 714? Round your answer to two decimal places. ​

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

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

At what y-value does the curve defined by have a vertical tangent? ​

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

Find the derivative of the following function. ​ ​

Find the derivative of the following function. ​ ​

Find implicitly for

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

Assume that s, r, and h are differentiable functions of t. If , find when , , , and . Round your answer to two decimal places. ​

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

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

Find the derivative of the following function. ​

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. ​

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

Assume that x and y are differentiable functions of t. A point is moving along the graph of the equation At what rate is y changing when and is changing at a rate of 4 units/sec? ​

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 dy/dx for the following equation: .

Find if

If , find .

Suppose the weekly demand function for a product is where p is the price in thousands of dollars and q is the number of units demanded. What is the elasticity of demand when the price is $1,000 and the quantity demanded is 714? Round your answer to two decimal places.

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

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

At what y-value does the curve defined by have a vertical tangent?

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

Find the derivative of the following function.

Find the derivative of the following function.

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

Assume that s, r, and h are differentiable functions of t. If , find when , , , and . Round your answer to two decimal places.

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

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

Find the derivative of the following function.

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.

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

Assume that x and y are differentiable functions of t. A point is moving along the graph of the equation At what rate is y changing when and is changing at a rate of 4 units/sec?