Question 1

Calculate   . You need not expand your answer.

Accepted Answer

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

Question 2

An offshore oil well is leaking oil and creating a circular oil slick. If the radius of the slick is growing at a rate of 7 miles per hour, find the rate at which the area is increasing when the radius is 6 miles. (The area of a disc of radius r is   .)

Accepted Answer

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

Question 3

Calculate   . You need not expand your answer.

Accepted Answer

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

Question 4

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 5

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

Accepted Answer

A) $5.00 per item 
B) $5.20 per item 
C) $4.80 per item 
D) $4.81 per item 
E) $4.78 per item 
A) $5.00 per item 
B) $5.20 per item 
C) $4.80 per item 
D) $4.81 per item 
E) $4.78 per item

Question 6

Calculate the derivative of the function.

Accepted Answer

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

Question 7

Compute the derivative.

Accepted Answer

A) 92 
B) 36 
C) 59 
D) 72 
E) 78 
A) 92 
B) 36 
C) 59 
D) 72 
E) 78

Question 8

Find   using implicit differentiation.

Accepted Answer

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

Question 9

Find the derivative of the function.

Accepted Answer

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

Question 10

Find   using implicit differentiation.

Accepted Answer

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

Question 11

The soap bubble I am blowing has a radius that is growing at a rate of 9 cm/s. How fast is the surface area growing when the radius is 14 cm? (The surface area of a sphere of radius r is   .)

Accepted Answer

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

Question 12

Find the derivative of the function.

Accepted Answer

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

Question 13

Calculate   . You need not expand your answer.

Accepted Answer

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

Question 14

Find   using implicit differentiation.

Accepted Answer

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

Question 15

Find the derivative of the function.

Accepted Answer

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

Question 16

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 17

Your Porsche s gas mileage (in miles per gallon)is given as a function M ( x )of speed x in miles per hour. It is found that   . Find M (30), M (70)and M (95).

Accepted Answer

A) M '(70)= 0.0049, M '(30)= 0, M '(95)= -0.000051 
B) M '(70)= 0.0049, M '(70)= 0, M '(95)= -0.000051 
C) M '(30)= 0.0049, M '(70)= 0, M '(95)= -0.000051 
D) M '(30)= 0.0001, M '(70)= -0.0049, M '(95)= 0 
E) M '(30)= 0.0001, M '(70)= 0, M '(95)= -0.0049 
A) M '(70)= 0.0049, M '(30)= 0, M '(95)= -0.000051 
B) M '(70)= 0.0049, M '(70)= 0, M '(95)= -0.000051 
C) M '(30)= 0.0049, M '(70)= 0, M '(95)= -0.000051 
D) M '(30)= 0.0001, M '(70)= -0.0049, M '(95)= 0 
E) M '(30)= 0.0001, M '(70)= 0, M '(95)= -0.0049

Question 18

Calculate   . You need not expand your answer.

Accepted Answer

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

Question 19

Evaluate the following derivative.

Accepted Answer

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

Question 20

Find the indicated derivative.   Please round the answer to the nearest hundredth.

Accepted Answer

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

Calculate . You need not expand your answer.

An offshore oil well is leaking oil and creating a circular oil slick. If the radius of the slick is growing at a rate of 7 miles per hour, find the rate at which the area is increasing when the radius is 6 miles. (The area of a disc of radius r is .)

Calculate . You need not expand your answer.

Find the derivative of the function.

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

Calculate the derivative of the function.

Compute the derivative.

Find using implicit differentiation.

Find the derivative of the function.

Find using implicit differentiation.

The soap bubble I am blowing has a radius that is growing at a rate of 9 cm/s. How fast is the surface area growing when the radius is 14 cm? (The surface area of a sphere of radius r is .)

Find the derivative of the function.

Calculate . You need not expand your answer.

Find using implicit differentiation.

Find the derivative of the function.

Find the derivative of the function.

Your Porsche s gas mileage (in miles per gallon)is given as a function M ( x )of speed x in miles per hour. It is found that . Find M (30), M (70)and M (95).

Calculate . You need not expand your answer.

Evaluate the following derivative.

Find the indicated derivative. Please round the answer to the nearest hundredth.

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

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Exam 4: Techniques of Differentiation With Applications

Calculate . You need not expand your answer.

An offshore oil well is leaking oil and creating a circular oil slick. If the radius of the slick is growing at a rate of 7 miles per hour, find the rate at which the area is increasing when the radius is 6 miles. (The area of a disc of radius r is .)

Calculate . You need not expand your answer.

Find the derivative of the function.

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

Calculate the derivative of the function.

Compute the derivative.

Find using implicit differentiation.

Find the derivative of the function.

Find using implicit differentiation.

The soap bubble I am blowing has a radius that is growing at a rate of 9 cm/s. How fast is the surface area growing when the radius is 14 cm? (The surface area of a sphere of radius r is .)

Find the derivative of the function.

Calculate . You need not expand your answer.

Find using implicit differentiation.

Find the derivative of the function.

Find the derivative of the function.

Your Porsche s gas mileage (in miles per gallon)is given as a function M ( x )of speed x in miles per hour. It is found that . Find M (30), M (70)and M (95).

Calculate . You need not expand your answer.

Evaluate the following derivative.

Find the indicated derivative. Please round the answer to the nearest hundredth.

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