Question 1

Find the equation of the straight line, tangent to   at the point (1, 0).

Accepted Answer

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

Question 2

Your Porche s gas mileage (in miles per gallon)is given as a function   of speed   in miles per hour.   Calculate   .

Accepted Answer

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

Question 3

The cost of producing x teddy bears per day at the Cuddly Companion Company is calculated by their marketing staff to be given by the formula   . Evaluate the average cost   .

Accepted Answer

A) $32.00 
B) $29.50 
C) $28.00 
D) $3,249.50 
E) $3,200.00 
A) $32.00 
B) $29.50 
C) $28.00 
D) $3,249.50 
E) $3,200.00

Question 4

Find the equation of the tangent line for   at the point   .

Accepted Answer

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

Question 5

Your company is planning to air a number of television commercials during the ABC television network s presentation of the Academy Awards. ABC is charging your company $795,000 per 30-second spot. Additional fixed costs (development and personnel costs)amount to $400,000, and the network has agreed to provide a discount of   for x television spots. Compute marginal cost   and average cost   .

Accepted Answer

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

Question 6

The oxygen consumption of a bird embryo increases from the time the egg is laid through the time the chick hatches. In a typical galliform bird, the oxygen consumption (in milliliters per hour)can be approximated by   where t is the time (in days)since the egg was laid. (An egg will typically hatch at around   .)Find   .

Accepted Answer

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

Question 7

The Thoroughbred Bus Company finds that its monthly costs for one particular year were given by   dollars after   months. After   months, the company had   passengers per month. How fast was its cost per passenger changing after   months?

Accepted Answer

A) $0.39 per month 
B) $0.01 per month 
C) -$0.18 per month 
D) $0.29 per month 
E) $0.10 per month 
A) $0.39 per month 
B) $0.01 per month 
C) -$0.18 per month 
D) $0.29 per month 
E) $0.10 per month

Question 8

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

A) no, 7 
B) yes, 7 
C) no, 0 
D) yes, 5 
E) yes, 0 
A) no, 7 
B) yes, 7 
C) no, 0 
D) yes, 5 
E) yes, 0

Question 9

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 10

Match between columns
                        Premises: 11ebfe6a_2ccf_3edd_96cc_616c8c3018a4_TBX8650_11
11ebfe6a_2ccf_17c9_96cc_8951e2a8b9da_TBX8650_11
11ebfe6a_2ccf_17c5_96cc_8db46dcbc1ef_TBX8650_11

Accepted Answer

The Answer of 11ebfe6a_2ccf_17c7_96cc_6904cae96381_TBX8650_11 and 11ebfe6a_2ccf_3edf_96cc_b51c46647967_TBX8650_11 and 11ebfe6a_2ccf_17c6_96cc_818d2ec768db_TBX8650_11 and 11ebfe6a_2ccf_17cc_96cc_5f312f5b553a_TBX8650_11 is...

Question 11

Compute the indicated derivative using the chain rule.

Accepted Answer

A) -4 
B) 8 
C)    
D) -2 
E)    
A) -4 
B) 8 
C)    
D) -2 
E)

Question 12

Find the value of x for which the marginal profit is zero.

Accepted Answer

A) x = -5,000 
B) x = 10,000 
C) x = 5,000 
D) x = 7,000 
E) x = 2,500 
A) x = -5,000 
B) x = 10,000 
C) x = 5,000 
D) x = 7,000 
E) x = 2,500

Question 13

Calculate the derivative of the function.   Please enter your answer as an expression.

Accepted Answer

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

Question 14

Evaluate the following derivative.

Accepted Answer

The answer of Evaluate the following derivative.  ...

Question 15

The cost of controlling emissions at a firm goes up rapidly as the amount of emissions reduced goes up. Here is a possible model:   where q is the reduction in emissions (in pounds of pollutant per day)and C is the daily cost (in dollars)of this reduction. Government clean-air subsidies to the firm are based on the formula   where q is again the reduction in emissions (in pounds per day)and S is the subsidy (in dollars). Calculate the net cost function   given the cost and subsidy above, and find the value of q that gives the lowest net cost. What is this lowest net cost?

Accepted Answer

A) q = $2, N ( q )= $2,300 
B) q = $4, N ( q )= $2,300 
C) q = $2, N ( q )= $4,600 
D) q = $2.5, N ( q )= $2,375 
E) q = $2.5, N ( q )= $2,300 
A) q = $2, N ( q )= $2,300 
B) q = $4, N ( q )= $2,300 
C) q = $2, N ( q )= $4,600 
D) q = $2.5, N ( q )= $2,375 
E) q = $2.5, N ( q )= $2,300

Question 16

Find   using implicit differentiation.

Accepted Answer

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

Question 17

Find the derivative of the function.

Accepted Answer

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

Question 18

The cost of controlling emissions at a firm goes up rapidly as the amount of emissions reduced goes up. Here is a possible model:   where q is the reduction in emissions (in pounds of pollutant per day)and C is the daily cost (in dollars)of this reduction. If a firm is currently reducing its emissions by 7 pounds each day, what is the marginal cost of reducing emissions even further?

Accepted Answer

A) $1,400 
B) $2,800 
C) $7,800 
D) $2,100 
E) $700 
A) $1,400 
B) $2,800 
C) $7,800 
D) $2,100 
E) $700

Question 19

If a stone is dropped from a height of 300 feet, its height s after t seconds is given by   with s in feet. a. Find the stone s velocity at   seconds. b. When does it reach the ground, and how fast is it travelling when it hits the ground? Round your answers to the nearest hundredth.

Accepted Answer

A) -100, 1.94, -77.46 
B) -10, 3.87, -600.00 
C) -200, 15.00, -600.00 
D) 200, 3.87, -154.92 
E) -200, 3.87, -154.92 
A) -100, 1.94, -77.46 
B) -10, 3.87, -600.00 
C) -200, 15.00, -600.00 
D) 200, 3.87, -154.92 
E) -200, 3.87, -154.92

Question 20

Compute the indicated derivative using the chain rule.

Accepted Answer

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

Find the equation of the straight line, tangent to at the point (1, 0).

Your Porche s gas mileage (in miles per gallon)is given as a function of speed in miles per hour. Calculate .

The cost of producing x teddy bears per day at the Cuddly Companion Company is calculated by their marketing staff to be given by the formula . Evaluate the average cost .

Find the equation of the tangent line for at the point .

The Thoroughbred Bus Company finds that its monthly costs for one particular year were given by dollars after months. After months, the company had passengers per month. How fast was its cost per passenger changing after months?

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

Find the derivative of the function.

Compute the indicated derivative using the chain rule.

Find the value of x for which the marginal profit is zero.

Calculate the derivative of the function. Please enter your answer as an expression.

Evaluate the following derivative.

Find using implicit differentiation.

Find the derivative of the function.

If a stone is dropped from a height of 300 feet, its height s after t seconds is given by with s in feet. a. Find the stone s velocity at seconds. b. When does it reach the ground, and how fast is it travelling when it hits the ground? Round your answers to the nearest hundredth.

Compute the indicated derivative using the chain rule.

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

Find the equation of the straight line, tangent to at the point (1, 0).

Your Porche s gas mileage (in miles per gallon)is given as a function of speed in miles per hour. Calculate .

The cost of producing x teddy bears per day at the Cuddly Companion Company is calculated by their marketing staff to be given by the formula . Evaluate the average cost .

Find the equation of the tangent line for at the point .

The Thoroughbred Bus Company finds that its monthly costs for one particular year were given by dollars after months. After months, the company had passengers per month. How fast was its cost per passenger changing after months?

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

Find the derivative of the function.

Compute the indicated derivative using the chain rule.

Find the value of x for which the marginal profit is zero.

Calculate the derivative of the function. Please enter your answer as an expression.

Evaluate the following derivative.

Find using implicit differentiation.

Find the derivative of the function.

If a stone is dropped from a height of 300 feet, its height s after t seconds is given by with s in feet. a. Find the stone s velocity at seconds. b. When does it reach the ground, and how fast is it travelling when it hits the ground? Round your answers to the nearest hundredth.

Compute the indicated derivative using the chain rule.

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