Question 1

Let f be the function defined by   . Find the approximate change in y if x changes from 1 to 1.08. Find the actual change in y if x changes from 1 to 1.08.

Accepted Answer

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

Question 2

The percent of mothers who work outside the home and have children younger than age 6 yr is approximated by the function   where t is measured in years, with t = 0 corresponding to the beginning of 1980. Compute   .

Accepted Answer

A)    per year in the second power 
B)    per year in the second power 
C)    per year in the second power 
D)    per year in the second power 
E)    per year in the second power 
A)    per year in the second power 
B)    per year in the second power 
C)    per year in the second power 
D)    per year in the second power 
E)    per year in the second power E

Question 3

Find the derivative of the function.

Accepted Answer

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

Question 4

Find   .

Accepted Answer

The answer of Find   .  ...

Question 5

Find the derivative of the function.

Accepted Answer

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

Question 6

Custom Office makes a line of executive desks. It is estimated that the total cost for making x units of their Senior Executive model is   dollars/year. Find the marginal average cost function   .

Accepted Answer

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

Question 7

Let f be the function defined by   . Use the differential of f to find the approximate change in y if x changes from 4 to 4.1.

Accepted Answer

A)  0.02774 
B)  0.36056 
C)  1.10940 
D)  0.05547 
E)  0.01387 
A)  0.02774 
B)  0.36056 
C)  1.10940 
D)  0.05547 
E)  0.01387

Question 8

Acrosonic's production department estimates that the total cost (in dollars) incurred in manufacturing x ElectroStat speaker systems in the first year of production will be   . The demand equation is   . Select the graph of the profit function.

Accepted Answer

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

Question 9

Suppose f and g are functions that are differentiable at   and that   ,   ,   , and   . Find the value of   .

Accepted Answer

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

Question 10

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

Accepted Answer

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

Question 11

A spectator watches a rowing race from the edge of a river bank. The lead boat is moving in a straight line that is 330 ft from the river bank. If the boat is moving at a constant speed of 20 ft/sec, how fast is the boat moving away from the spectator when it is 560 ft past her?
Round the answer to the nearest hundredth, if necessary.
__________ ft/sec

Accepted Answer

The answer of A spectator watches a rowing race from...

Question 12

Find the first and second derivatives of the function.

Accepted Answer

The answer of Find the first and second derivatives of...

Question 13

The total weekly cost (in dollars) incurred by a company in pressing x compact discs is   . What is the marginal cost when   and   ?

Accepted Answer

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

Question 14

An economy's consumer price index (CPI) is described by the function   , where   corresponds to 1995. At what rate was the CPI changing in 2002?

Accepted Answer

A)  12.3 pts/yr 
B)  12.6 pts/yr 
C)  12.5 pts/yr 
D)  12.4 pts/yr 
E)  12.7 pts/yr 
A)  12.3 pts/yr 
B)  12.6 pts/yr 
C)  12.5 pts/yr 
D)  12.4 pts/yr 
E)  12.7 pts/yr

Question 15

Find the derivative of the function.

Accepted Answer

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

Question 16

A 5-ft tall man is walking away from a street light 10 ft high at a speed of 4 ft/sec . How fast is the tip of his shadow moving along the ground?
__________ ft/sec

Accepted Answer

The answer of A 5-ft tall man is walking away...

Question 17

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

Accepted Answer

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

Question 18

Find the derivative of the function.

Accepted Answer

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

Question 19

Find   by implicit differentiation.

Accepted Answer

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

Question 20

Find the derivative of the function.

Accepted Answer

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

Let f be the function defined by . Find the approximate change in y if x changes from 1 to 1.08. Find the actual change in y if x changes from 1 to 1.08.

The percent of mothers who work outside the home and have children younger than age 6 yr is approximated by the function where t is measured in years, with t = 0 corresponding to the beginning of 1980. Compute .

Find the derivative of the function.

Find .

Find the derivative of the function.

Custom Office makes a line of executive desks. It is estimated that the total cost for making x units of their Senior Executive model is dollars/year. Find the marginal average cost function .

Let f be the function defined by . Use the differential of f to find the approximate change in y if x changes from 4 to 4.1.

Acrosonic's production department estimates that the total cost (in dollars) incurred in manufacturing x ElectroStat speaker systems in the first year of production will be . The demand equation is . Select the graph of the profit function.

Suppose f and g are functions that are differentiable at and that , , , and . Find the value of .

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

Find the first and second derivatives of the function.

The total weekly cost (in dollars) incurred by a company in pressing x compact discs is . What is the marginal cost when and ?

An economy's consumer price index (CPI) is described by the function , where corresponds to 1995. At what rate was the CPI changing in 2002?

Find the derivative of the function.

A 5-ft tall man is walking away from a street light 10 ft high at a speed of 4 ft/sec . How fast is the tip of his shadow moving along the ground? __________ ft/sec

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

Find the derivative of the function.

Find by implicit differentiation.

Find the derivative of the function.

Preliminaries

Functions, Limits and the Derivative

Applications of the Derivative

Exponential and Logarithmic Functions

Integration

Additional Topics in Integration

Calculus of Several Variables

Filters

Exam 3: Differentiation

Let f be the function defined by . Find the approximate change in y if x changes from 1 to 1.08. Find the actual change in y if x changes from 1 to 1.08.

The percent of mothers who work outside the home and have children younger than age 6 yr is approximated by the function where t is measured in years, with t = 0 corresponding to the beginning of 1980. Compute .

Find the derivative of the function.

Find .

Find the derivative of the function.

Custom Office makes a line of executive desks. It is estimated that the total cost for making x units of their Senior Executive model is dollars/year. Find the marginal average cost function .

Let f be the function defined by . Use the differential of f to find the approximate change in y if x changes from 4 to 4.1.

Acrosonic's production department estimates that the total cost (in dollars) incurred in manufacturing x ElectroStat speaker systems in the first year of production will be . The demand equation is . Select the graph of the profit function.

Suppose f and g are functions that are differentiable at and that , , , and . Find the value of .

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

Find the first and second derivatives of the function.

The total weekly cost (in dollars) incurred by a company in pressing x compact discs is . What is the marginal cost when and ?

An economy's consumer price index (CPI) is described by the function , where corresponds to 1995. At what rate was the CPI changing in 2002?

Find the derivative of the function.

A 5-ft tall man is walking away from a street light 10 ft high at a speed of 4 ft/sec . How fast is the tip of his shadow moving along the ground? __________ ft/sec

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

Find the derivative of the function.

Find by implicit differentiation.

Find the derivative of the function.

Preliminaries

Functions, Limits and the Derivative

Applications of the Derivative

Exponential and Logarithmic Functions

Integration

Additional Topics in Integration

Calculus of Several Variables

Filters