Question 1

Find the slope of the tangent to the graph of the given function   at the point   .

Accepted Answer

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

Question 2

An employment research company estimates that the value of a recent MBA graduate to an accounting company is   where   is the value of the graduate,   is a number of years of prior business experience, and   is the graduate school grade point average. If   , find   when   . All the answers were rounded to the nearest hundredth.

Accepted Answer

A) -2.77 
B) -1.56 
C) -0.23 
D) -0.11 
E) 0.11 
A) -2.77 
B) -1.56 
C) -0.23 
D) -0.11 
E) 0.11

Question 3

Find the derivative of the function.

Accepted Answer

A)    
B)    
C)    
D)    
E) none of these 
A)    
B)    
C)    
D)    
E) none of these

Question 4

The Verhulst model for population growth specifies the reproductive rate of an organism as a function of the total population according to the following formula:   where p is the total population in thousands of organisms,   and   are constants that depend on the particular circumstances and organism being studied, and   is the reproduction rate in thousands of organisms per hour. If   and   , find   .

Accepted Answer

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

Question 5

Find   using implicit differentiation.

Accepted Answer

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

Question 6

Compute the indicated derivative using the chain rule.

Accepted Answer

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

Question 7

The population of Upper Anchora was 2,000,000 at the start of 1996 and was doubling every 10 years. How fast was it growing per year at the start of 1996? Round your answer to the nearest thousand.

Accepted Answer

A) 138,000 people per year 
B) 129,000 people per year 
C) 139,000 people per year 
D) 140,000 people per year 
E) 278,000 people per year 
A) 138,000 people per year 
B) 129,000 people per year 
C) 139,000 people per year 
D) 140,000 people per year 
E) 278,000 people per year

Question 8

Find all the values of x (if any)where the tangent line to the graph of the given equation is horizontal.

Accepted Answer

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

Question 9

Use logarithmic differentiation to find   . Do not simplify the result.

Accepted Answer

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

Question 10

Find the equation of the line tangent to the graph of the given function at the point   .

Accepted Answer

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

Question 11

Find the derivative of the function.

Accepted Answer

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

Question 12

The number P of CDs the Snappy Hardware Co. can manufacture at its plant in one day is given by   where x is the number of workers at the plant and y is the annual expenditure at the plant (in dollars). Compute   at a production level of 24,000 CDs per day and   .

Accepted Answer

The answer of The number P of CDs the Snappy...

Question 13

Find the derivative of the following function.

Accepted Answer

The answer of Find the derivative of the following function....

Question 14

Find the indicated derivative. The independent variable is a function of   .

Accepted Answer

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

Question 15

Find the derivative of the function.

Accepted Answer

The answer of Find the derivative of the function. ...

Question 16

The monthly sales of Sunny Electronics new stereo system is given by   hundred units per month,   months after its introduction. The price Sunny charges is   dollars per stereo system,   months after its introduction. The revenue Sunny earns then must be   . Find the rate of change of revenue   months after introduction.

Accepted Answer

A) -$473,000 per month 
B) -$567,500 per month 
C) $31,840 per month 
D) $318,400 per month 
E) $197,600 per month 
A) -$473,000 per month 
B) -$567,500 per month 
C) $31,840 per month 
D) $318,400 per month 
E) $197,600 per month

Question 17

Find the derivative of the function.

Accepted Answer

The answer of Find the derivative of the function. ...

Question 18

Find the derivative of the function.

Accepted Answer

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

Question 19

Use the shortcut rules to calculate the derivative of the given function.

Accepted Answer

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

Question 20

Find   using implicit differentiation.

Accepted Answer

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

Find the slope of the tangent to the graph of the given function at the point .

Find the derivative of the function.

Find using implicit differentiation.

Compute the indicated derivative using the chain rule.

The population of Upper Anchora was 2,000,000 at the start of 1996 and was doubling every 10 years. How fast was it growing per year at the start of 1996? Round your answer to the nearest thousand.

Find all the values of x (if any)where the tangent line to the graph of the given equation is horizontal.

Use logarithmic differentiation to find . Do not simplify the result.

Find the equation of the line tangent to the graph of the given function at the point .

Find the derivative of the function.

The number P of CDs the Snappy Hardware Co. can manufacture at its plant in one day is given by where x is the number of workers at the plant and y is the annual expenditure at the plant (in dollars). Compute at a production level of 24,000 CDs per day and .

Find the derivative of the following function.

Find the indicated derivative. The independent variable is a function of .

Find the derivative of the function.

Find the derivative of the function.

Find the derivative of the function.

Use the shortcut rules to calculate the derivative of the given function.

Find using implicit differentiation.

Functions and Linear Models

Nonlinear Functions and Models

Introduction to the Derivative

Further Applications of the Derivative

The Integral

Further Integration Techniques and Applications of the Integral

Functions of Several Variables

Trigonometric Models

Filters

Exam 4: Techniques of Differentiation With Applications

Find the slope of the tangent to the graph of the given function at the point .

Find the derivative of the function.

Find using implicit differentiation.

Compute the indicated derivative using the chain rule.

The population of Upper Anchora was 2,000,000 at the start of 1996 and was doubling every 10 years. How fast was it growing per year at the start of 1996? Round your answer to the nearest thousand.

Find all the values of x (if any)where the tangent line to the graph of the given equation is horizontal.

Use logarithmic differentiation to find . Do not simplify the result.

Find the equation of the line tangent to the graph of the given function at the point .

Find the derivative of the function.

The number P of CDs the Snappy Hardware Co. can manufacture at its plant in one day is given by where x is the number of workers at the plant and y is the annual expenditure at the plant (in dollars). Compute at a production level of 24,000 CDs per day and .

Find the derivative of the following function.

Find the indicated derivative. The independent variable is a function of .

Find the derivative of the function.

Find the derivative of the function.

Find the derivative of the function.

Use the shortcut rules to calculate the derivative of the given function.

Find using implicit differentiation.

Functions and Linear Models

Nonlinear Functions and Models

Introduction to the Derivative

Further Applications of the Derivative

The Integral

Further Integration Techniques and Applications of the Integral

Functions of Several Variables

Trigonometric Models

Filters