Question 1

Find the derivative of the function.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 2

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

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 3

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. Please enter your answer in dollars/month without the units.

Accepted Answer

The answer of The monthly sales of Sunny Electronics new...

Question 4

Calculate  . You need not expand your answer.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 5

Find  using implicit differentiation.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 6

Your monthly profit (in dollars)from selling magazines is given by  where x is the number of magazines you sell in a month. If you are currently selling x = 100 magazines per month, find your profit and your marginal profit.

Accepted Answer

A) P (100)= $215, P '(100)= $2.08 
B) P (100)= $430, P '(100)= $4.15 
C) P (100)= $417.32, P '(100)= $0.35 
D) P (100)= $417.32, P '(100)= $4.15 
E) P (100)= $860, P '(100)= $4.65

Question 7

Use logarithmic differentiation to find  .

Accepted Answer

The answer of Use logarithmic differentiation to find  ....

Question 8

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

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 9

Find the derivative of the function.

Accepted Answer

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

Question 10

Find  using implicit differentiation.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 11

Given.  Say whether L Hospital s rule applies. __________ It is does, use it to evaluate the given limit. If not, use some other method. __________

Accepted Answer

The answer of Given.  Say whether L Hospital s...

Question 12

Calculate  .

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 13

The Pentagon is planning to build a new satellite that will be spherical. As is typical in these cases, the specifications keep changing, so that the size of the satellite keeps growing. In fact, the radius of the planned satellite is growing 0.5 foot/week. Its cost will be $1,000 per cubic foot. At the point when the plans call for a satellite 5 feet in radius, how fast is the cost growing? (The volume of a solid sphere of radius r is  .)

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 14

The demand for the Cyberpunk II arcade video game is modeled by the logistic curve  where q ( t )is the total number of units sold t months after the game s introduction. Use technology to estimate  . Assume that the manufacturers of Cyberpunk II sell each unit for $600. What is the company s marginal revenue,  ? Use the chain rule to estimate the rate at which revenue is growing 5 months after the introduction of the video game. Please round each answer to the nearest whole number.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 15

For the cost function C ( x ), find the marginal cost at the given production level x .

Accepted Answer

A) $39.96 per item 
B) $49.95 per item 
C) $49.97 per item 
D) $51.25 per item 
E) $40.00 per item

Question 16

Find  using implicit differentiation.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 17

Calculate the derivative of the function.

Accepted Answer

The answer of Calculate the derivative of the function. ...

Question 18

Calculate  .

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 19

Calculate the derivative of the function.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 20

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

Accepted Answer

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

Exam 4: Techniques of Differentiation With Applications

Find the derivative of the function.

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

Calculate . You need not expand your answer.

Find using implicit differentiation.

Your monthly profit (in dollars) from selling magazines is given by where x is the number of magazines you sell in a month. If you are currently selling x = 100 magazines per month, find your profit and your marginal profit.

Use logarithmic differentiation to find .

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

Find the derivative of the function.

Find using implicit differentiation.

Given. Say whether L Hospital s rule applies. It is does, use it to evaluate the given limit. If not, use some other method.

Calculate .

For the cost function C ( x ) , find the marginal cost at the given production level x .

Find using implicit differentiation.

Calculate the derivative of the function.

Calculate .

Calculate the derivative of the function.

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