Question 1

Differentiate   . Assume b is a positive constant.

Accepted Answer

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

Question 2

Find   if   .

Accepted Answer

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

Question 3

The amount, W, of fuel used by an aircraft flying at speed v km/min is given, in liters, by   . Find the rate of change of W with respect to v when v = 4. Round to 1 decimal place.

Accepted Answer

The answer of The amount, W, of fuel used by...

Question 4

Find the first derivative of   .

Accepted Answer

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

Question 5

Find the first derivative of w(x) = bx2 + xu.

Accepted Answer

A) x2 + uxu-1 
B) 2bx + ux 
C) 2bx + u 
D) 2bx + uxu-1 
A) x2 + uxu-1 
B) 2bx + ux 
C) 2bx + u 
D) 2bx + uxu-1

Question 6

The first derivative of   is   .

Accepted Answer

A) True 
 B)False

Question 7

Compute the derivative of   .

Accepted Answer

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

Question 8

Find the first derivative of   .

Accepted Answer

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

Question 9

The derivative of   is   .

Accepted Answer

A) True 
 B)False

Question 10

Find the derivative of   .

Accepted Answer

The answer of Find the derivative of   ....

Question 11

Find x where the derivative of   is equal to zero.

Accepted Answer

The answer of Find x where the derivative of ...

Question 12

Find the derivative of   .

Accepted Answer

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

Question 13

A. Find the equation of the line tangent to the graph of   at   .
B. Find the x-intercept of this line.
C. Find the y-intercept of this line.

Accepted Answer

The answer of A. Find the equation of the line...

Question 14

The equation of the tangent line to   at the point where   is given by   .

Accepted Answer

A) True 
 B)False

Question 15

The size of an impala population is represented by the function   , where t is time in months since the beginning of the year and   is measured in thousands. After 7 months, the population is __________(increasing/decreasing) at a rate of _____ thousand per month. Round to 2 decimal places.

Accepted Answer

Part A: in

Question 16

The total cost, in dollars, to produce q units is given by   . Find

Accepted Answer

The answer of The total cost, in dollars, to produce...

Question 17

The population of a town is approximated by the function   , where t is the number of years since 1980. Find   . Round to the nearest whole number.

Accepted Answer

The answer of The population of a town is approximated...

Question 18

The first derivative of   is

Accepted Answer

A) True 
 B)False

Question 19

The value of a car is falling at 10% per year so that if   is the purchase price of the car in dollars, its value after t years is given by   . How fast is the car depreciating after 4 years?

Accepted Answer

A)    dollars per year 
B)    dollars per year 
C)    dollars per year 
D)    dollars per year 
A)    dollars per year 
B)    dollars per year 
C)    dollars per year 
D)    dollars per year

Question 20

Find the derivative of   .

Accepted Answer

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

Differentiate . Assume b is a positive constant.

Find if .

The amount, W, of fuel used by an aircraft flying at speed v km/min is given, in liters, by . Find the rate of change of W with respect to v when v = 4. Round to 1 decimal place.

Find the first derivative of .

Find the first derivative of w(x) = bx²+ x^u^.

The first derivative of is .

Compute the derivative of .

Find the first derivative of .

The derivative of is .

Find the derivative of .

Find x where the derivative of is equal to zero.

Find the derivative of .

A. Find the equation of the line tangent to the graph of at . B. Find the x-intercept of this line. C. Find the y-intercept of this line.

The equation of the tangent line to at the point where is given by .

The size of an impala population is represented by the function , where t is time in months since the beginning of the year and is measured in thousands. After 7 months, the population is ______(increasing/decreasing) at a rate of _ thousand per month. Round to 2 decimal places.

The total cost, in dollars, to produce q units is given by . Find

The population of a town is approximated by the function , where t is the number of years since 1980. Find . Round to the nearest whole number.

The first derivative of is

The value of a car is falling at 10% per year so that if is the purchase price of the car in dollars, its value after t years is given by . How fast is the car depreciating after 4 years?

Find the derivative of .

Functions and Change

Rate of Change: the Derivative

Using the Derivative

Accumulated Change: the Definite Integral

Antiderivatives and Applications

Probability

Functions of Several Variables

Mathematical Modeling Using Differential Equations

Geometric Series

Filters

Exam 3: Shortcuts to Differentiation

Differentiate . Assume b is a positive constant.

Find if .

The amount, W, of fuel used by an aircraft flying at speed v km/min is given, in liters, by . Find the rate of change of W with respect to v when v = 4. Round to 1 decimal place.

Find the first derivative of .

Find the first derivative of w(x) = bx2 + xu.

The first derivative of is .

Compute the derivative of .

Find the first derivative of .

The derivative of is .

Find the derivative of .

Find x where the derivative of is equal to zero.

Find the derivative of .

A. Find the equation of the line tangent to the graph of at . B. Find the x-intercept of this line. C. Find the y-intercept of this line.

The equation of the tangent line to at the point where is given by .

The size of an impala population is represented by the function , where t is time in months since the beginning of the year and is measured in thousands. After 7 months, the population is __________(increasing/decreasing) at a rate of _____ thousand per month. Round to 2 decimal places.

The total cost, in dollars, to produce q units is given by . Find

The population of a town is approximated by the function , where t is the number of years since 1980. Find . Round to the nearest whole number.

The first derivative of is

The value of a car is falling at 10% per year so that if is the purchase price of the car in dollars, its value after t years is given by . How fast is the car depreciating after 4 years?

Find the derivative of .

Functions and Change

Rate of Change: the Derivative

Using the Derivative

Accumulated Change: the Definite Integral

Antiderivatives and Applications

Probability

Functions of Several Variables

Mathematical Modeling Using Differential Equations

Geometric Series

Filters

Find the first derivative of w(x) = bx²+ x^u^.

The size of an impala population is represented by the function , where t is time in months since the beginning of the year and is measured in thousands. After 7 months, the population is ______(increasing/decreasing) at a rate of _ thousand per month. Round to 2 decimal places.