Question 1

A certain producer determines that his cost function is   . Determine the average cost of producing 1500 units. Round answer to the nearest penny.

Accepted Answer

A)  $5.38 
B)  $6.16 
C)  $7.10 
D)  $8.27 
A)  $5.38 
B)  $6.16 
C)  $7.10 
D)  $8.27

Question 2

Newton's method fails for the given initial guess. Explain why the method fails and, if possible, find a root by correcting the problem. Round to four decimal places, if necessary.   , x0 = -1

Accepted Answer

A)  f '(-1) = 0; -1.905, 0.105 
B)  f '(-1) does not exist; -1.905, 0.105 
C)  f (-1) = 0; 1.905, -0.105 
D)  f (-1) does not exist; 1.905, -0.105 
A)  f '(-1) = 0; -1.905, 0.105 
B)  f '(-1) does not exist; -1.905, 0.105 
C)  f (-1) = 0; 1.905, -0.105 
D)  f (-1) does not exist; 1.905, -0.105

Question 3

Find the intervals where the function is increasing and decreasing on the specified interval. Use this information to determine all local extrema.   on

Accepted Answer

decreasing: @#IMG-DLM& ; incre

Question 4

Given   , determine the critical number(s).

Accepted Answer

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

Question 5

Find the linear approximation, L(x), to f(x) at x = x0.

Accepted Answer

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

Question 6

Determine the following significant features of   , approximating if necessary, and sketch the graph.
a). intercepts b). asymptotes
c). extrema d). inflection points

Accepted Answer

@#IMG-DLM& a. Domain @#IMG-DLM& Range @#IMG-DLM& b. intercep

Question 7

Given   , determine the absolute extrema on the interval   .

Accepted Answer

A)  absolute max:   ; absolute min:   
B)  absolute max:   and   ; absolute min:   and   
C)  absolute max:   ; absolute min:   
D)  absolute max:   ; absolute min:   
A)  absolute max:   ; absolute min:   
B)  absolute max:   and   ; absolute min:   and   
C)  absolute max:   ; absolute min:   
D)  absolute max:   ; absolute min:

Question 8

Determine all critical numbers of   .

Accepted Answer

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

Question 9

Oil spills out of a tanker at the rate of 145 gallons per minute. The oil spreads in a circle with a thickness of 1/4 inch. Given that 1 ft3 equals 7.5 gallons, determine the rate at which the radius of the spill is increasing when the radius reaches 90 feet.

Accepted Answer

A)  12.308 ft/min 
B)  3.282 ft/min 
C)  1.641 ft/min 
D)  1.611 ft/min 
A)  12.308 ft/min 
B)  3.282 ft/min 
C)  1.641 ft/min 
D)  1.611 ft/min

Question 10

Determine the intervals where   is concave up and concave down. Round answers to nearest hundredth.

Accepted Answer

A)  concave up for   concave down for   
B)  concave down for   concave up for   
C)  concave up for   
D)  concave down for   concave up for   
A)  concave up for   concave down for   
B)  concave down for   concave up for   
C)  concave up for   
D)  concave down for   concave up for

Question 11

Using the critical numbers of   , use the Second Derivative Test to determine all local extrema.

Accepted Answer

A)  critical numbers:   ; local max   ; local min   
B)  critical numbers:   ; local max   ; local min   
C)  critical numbers:   ; local max   ; local min   
D)  critical numbers:   ; local max   ; local min   
A)  critical numbers:   ; local max   ; local min   
B)  critical numbers:   ; local max   ; local min   
C)  critical numbers:   ; local max   ; local min   
D)  critical numbers:   ; local max   ; local min

Question 12

A person in a rowboat 2 miles from the nearest point on a straight shoreline wishes to reach his house which is 6 miles farther down the shore. If he can row at a rate of 6 miles per hour and run at a rate of 10 miles per hour, what is the minimum amount of time (in minutes) it will take him to get home?

Accepted Answer

A)  68 minutes 
B)  45 minutes 
C)  52 minutes 
D)  73 minutes 
A)  68 minutes 
B)  45 minutes 
C)  52 minutes 
D)  73 minutes

Question 13

A ladder 36 feet long is leaning against a vertical wall. If the bottom of the ladder is pulled away from the base of the building at a rate of 3 ft/sec, how fast is the top of the ladder sliding down the wall when it is 28 feet above the ground? Round answer to nearest tenth.

Accepted Answer

A)  2.4 ft/sec 
B)  2.2 ft/sec 
C)  2.0 ft/sec 
D)  1.8 ft/sec 
A)  2.4 ft/sec 
B)  2.2 ft/sec 
C)  2.0 ft/sec 
D)  1.8 ft/sec

Question 14

Approximate   accurate to 3 decimal places using Newton's method. State the function used.

Accepted Answer

A)  2.289 using   
B)  2.359 using   
C)  2.219 using   
D)  2.289 using   
A)  2.289 using   
B)  2.359 using   
C)  2.219 using   
D)  2.289 using

Question 15

Find the point on the curve   closest to the point   .

Accepted Answer

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

Question 16

Suppose that the body temperature 30 minutes after receiving x mg of a drug is given by   for   . The absolute value of the derivative,   , is defined as the sensitivity of the body to the drug dosage. Find the dosage that maximizes sensitivity.

Accepted Answer

A)  x = 4 mg 
B)  x = 6 mg 
C)  x = 2 mg 
D)  x = 3 mg 
A)  x = 4 mg 
B)  x = 6 mg 
C)  x = 2 mg 
D)  x = 3 mg

Question 17

Determine all significant features and sketch a graph.

Accepted Answer

domain: @#IMG-DLM& range: @#IMG-DLM& x-intercepts:

Question 18

Determine the following significant features by hand and sketch the graph of   .
a). intercepts
b). asymptotes
c). extrema
d). inflection points

Accepted Answer

@#IMG-DLM& ; x-int(s): x @#IMG-DLM& ; vertical asy

Question 19

A rectangle has its two bottom corners lying on the x-axis and the two top corners on the parabola   , where   . If the area of the rectangle is to be maximized, then what are its dimensions?

Accepted Answer

A)  1   3 
B)  2   2 
C)  4   5 
D)  1   2 
A)  1   3 
B)  2   2 
C)  4   5 
D)  1   2

Question 20

Find the elasticity of demand if   .

Accepted Answer

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

A certain producer determines that his cost function is . Determine the average cost of producing 1500 units. Round answer to the nearest penny.

Newton's method fails for the given initial guess. Explain why the method fails and, if possible, find a root by correcting the problem. Round to four decimal places, if necessary. , x₀ = -1

Find the intervals where the function is increasing and decreasing on the specified interval. Use this information to determine all local extrema. on

Given , determine the critical number(s).

Find the linear approximation, L(x), to f(x) at x = x₀.

Determine the following significant features of , approximating if necessary, and sketch the graph. a). intercepts b). asymptotes c). extrema d). inflection points

Given , determine the absolute extrema on the interval .

Determine all critical numbers of .

Oil spills out of a tanker at the rate of 145 gallons per minute. The oil spreads in a circle with a thickness of 1/4 inch. Given that 1 ft³ equals 7.5 gallons, determine the rate at which the radius of the spill is increasing when the radius reaches 90 feet.

Determine the intervals where is concave up and concave down. Round answers to nearest hundredth.

Using the critical numbers of , use the Second Derivative Test to determine all local extrema.

A ladder 36 feet long is leaning against a vertical wall. If the bottom of the ladder is pulled away from the base of the building at a rate of 3 ft/sec, how fast is the top of the ladder sliding down the wall when it is 28 feet above the ground? Round answer to nearest tenth.

Approximate accurate to 3 decimal places using Newton's method. State the function used.

Find the point on the curve closest to the point .

Suppose that the body temperature 30 minutes after receiving x mg of a drug is given by for . The absolute value of the derivative, , is defined as the sensitivity of the body to the drug dosage. Find the dosage that maximizes sensitivity.

Determine all significant features and sketch a graph.

Determine the following significant features by hand and sketch the graph of . a). intercepts b). asymptotes c). extrema d). inflection points

A rectangle has its two bottom corners lying on the x-axis and the two top corners on the parabola , where . If the area of the rectangle is to be maximized, then what are its dimensions?

Find the elasticity of demand if .

Preliminaries

Limits and Continuity

Differentiation

Integration

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

Integration Techniques

First-Order Differential Equations

Infinite Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

Filters

Exam 4: Applications of the Derivative

A certain producer determines that his cost function is . Determine the average cost of producing 1500 units. Round answer to the nearest penny.

Newton's method fails for the given initial guess. Explain why the method fails and, if possible, find a root by correcting the problem. Round to four decimal places, if necessary. , x0 = -1

Find the intervals where the function is increasing and decreasing on the specified interval. Use this information to determine all local extrema. on

Given , determine the critical number(s).

Find the linear approximation, L(x), to f(x) at x = x0.

Determine the following significant features of , approximating if necessary, and sketch the graph. a). intercepts b). asymptotes c). extrema d). inflection points

Given , determine the absolute extrema on the interval .

Determine all critical numbers of .

Oil spills out of a tanker at the rate of 145 gallons per minute. The oil spreads in a circle with a thickness of 1/4 inch. Given that 1 ft3 equals 7.5 gallons, determine the rate at which the radius of the spill is increasing when the radius reaches 90 feet.

Determine the intervals where is concave up and concave down. Round answers to nearest hundredth.

Using the critical numbers of , use the Second Derivative Test to determine all local extrema.

A ladder 36 feet long is leaning against a vertical wall. If the bottom of the ladder is pulled away from the base of the building at a rate of 3 ft/sec, how fast is the top of the ladder sliding down the wall when it is 28 feet above the ground? Round answer to nearest tenth.

Approximate accurate to 3 decimal places using Newton's method. State the function used.

Find the point on the curve closest to the point .

Suppose that the body temperature 30 minutes after receiving x mg of a drug is given by for . The absolute value of the derivative, , is defined as the sensitivity of the body to the drug dosage. Find the dosage that maximizes sensitivity.

Determine all significant features and sketch a graph.

Determine the following significant features by hand and sketch the graph of . a). intercepts b). asymptotes c). extrema d). inflection points

A rectangle has its two bottom corners lying on the x-axis and the two top corners on the parabola , where . If the area of the rectangle is to be maximized, then what are its dimensions?

Find the elasticity of demand if .

Preliminaries

Limits and Continuity

Differentiation

Integration

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

Integration Techniques

First-Order Differential Equations

Infinite Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

Filters

Newton's method fails for the given initial guess. Explain why the method fails and, if possible, find a root by correcting the problem. Round to four decimal places, if necessary. , x₀ = -1

Find the linear approximation, L(x), to f(x) at x = x₀.

Oil spills out of a tanker at the rate of 145 gallons per minute. The oil spreads in a circle with a thickness of 1/4 inch. Given that 1 ft³ equals 7.5 gallons, determine the rate at which the radius of the spill is increasing when the radius reaches 90 feet.