Question 1

What is the minimum value of   ? Restrict your attention to the horizontal span of 0 to 10.Round your answer to two decimal places. ​

Accepted Answer

A)  30.15 
B)  6.11 
C)  33.72 
D)  4.22 
A)  30.15 
B)  6.11 
C)  33.72 
D)  4.22

Question 2

What is the maximum value of   ? Restrict your attention to the horizontal span of 0 to 4.Round your answer to two decimal places. ​

Accepted Answer

A)  41.14 
B)  2.92 
C)  186.00 
D)  1.78 
A)  41.14 
B)  2.92 
C)  186.00 
D)  1.78

Question 3

Find the maximum value of   .Restrict your attention to the horizontal span of 0 to 10.Round your answer to two decimal places. ​

Accepted Answer

A)  2.50 
B)  0.72 
C)  4.14 
D)  4.42 
A)  2.50 
B)  0.72 
C)  4.14 
D)  4.42

Question 4

You put a drink in the freezer to cool.When it is chilled, you take the drink out but, being forgetful, leave it sitting on the kitchen counter.The temperature D, in degrees, of the drink t minutes after it is put in the freezer is given by ​   .
​
During the period from 5 minutes after it is put in the freezer until 20 minutes after, when is the drink the warmest, and what is its warmest temperature? Be careful.You are asked for the warmest temperature, not the coldest.Round your answers to two decimal places.
​

Accepted Answer

A)  It reaches its warmest temperature of 45.13 degrees after 5.00 minutes. 
B)  It reaches its warmest temperature of 5.00 degrees after 45.13 minutes. 
C)  It reaches its warmest temperature of 20.00 degrees after 54.93 minutes. 
D)  It reaches its warmest temperature of 54.93 degrees after 20.00 minutes. 
A)  It reaches its warmest temperature of 45.13 degrees after 5.00 minutes. 
B)  It reaches its warmest temperature of 5.00 degrees after 45.13 minutes. 
C)  It reaches its warmest temperature of 20.00 degrees after 54.93 minutes. 
D)  It reaches its warmest temperature of 54.93 degrees after 20.00 minutes.

Question 5

You are laying phone cable between two cities and must cross a lake.You will lay L miles on land.The cost C, in dollars, depends on how much cable is on land and how much is in water.The relationship is   . ​
How much cable do you lay on land to achieve a minimum cost, and what is that minimum cost? Round your answers to two decimal places.
​

Accepted Answer

A)  The minimum cost of $7.25 is achieved if you lay 2543.73 miles of cable on land. 
B)  The minimum cost of $2543.73 is achieved if you lay 7.25 miles of cable on land. 
C)  The minimum cost of $5.32 is achieved if you lay 2541.63 miles of cable on land. 
D)  The minimum cost of $2541.63 is achieved if you lay 5.32 miles of cable on land. 
A)  The minimum cost of $7.25 is achieved if you lay 2543.73 miles of cable on land. 
B)  The minimum cost of $2543.73 is achieved if you lay 7.25 miles of cable on land. 
C)  The minimum cost of $5.32 is achieved if you lay 2541.63 miles of cable on land. 
D)  The minimum cost of $2541.63 is achieved if you lay 5.32 miles of cable on land.

Question 6

What value of x gives the maximum value of   ? Restrict your attention to the horizontal span of 0 to 10.Round your answer to two decimal places. ​

Accepted Answer

A)  2.86 
B)  1.22 
C)  4.72 
D)  4.74 
A)  2.86 
B)  1.22 
C)  4.72 
D)  4.74

Question 7

You put a drink in the freezer to cool.When it is chilled, you take the drink out but, being forgetful, leave it sitting on the kitchen counter.The temperature D, in degrees, of the drink t minutes after it is put in the freezer is given by ​   .
​
When during the first 20 minutes is the drink the warmest, and what is its warmest temperature? Be careful.You are asked for the warmest temperature, not the coldest.Round your answers to two decimal places.
​

Accepted Answer

A)  It reaches its warmest temperature of 72.00 degrees when it is first put in the freezer. 
B)  It reaches its warmest temperature of 0.00 degrees when it is first put in the freezer. 
C)  It reaches its warmest temperature of 20.00 degrees after 54.93 minutes. 
D)  It reaches its warmest temperature of 54.93 degrees after 20.00 minutes. 
A)  It reaches its warmest temperature of 72.00 degrees when it is first put in the freezer. 
B)  It reaches its warmest temperature of 0.00 degrees when it is first put in the freezer. 
C)  It reaches its warmest temperature of 20.00 degrees after 54.93 minutes. 
D)  It reaches its warmest temperature of 54.93 degrees after 20.00 minutes.

Question 8

Assume that the function   is increasing on the horizontal span of 2 to 25.Then the maximum value of   on this horizontal span is   .

Accepted Answer

A) True 
 B)False

Question 9

You put a drink in the freezer to cool.When it is chilled, you take the drink out but, being forgetful, leave it sitting on the kitchen counter.The temperature D, in degrees, of the drink t minutes after it is put in the freezer is given by ​   .
​
When is the drink the coldest, and what is its coldest temperature? Round your answers to two decimal places.
​

Accepted Answer

A)  It reaches its coldest temperature of 9.76 degrees after 25.76 minutes. 
B)  It reaches its coldest temperature of 25.76 degrees after 9.76 minutes. 
C)  It reaches its coldest temperature of 12.37 degrees after 29.30 minutes. 
D)  It reaches its coldest temperature of 29.30 degrees after 12.37 minutes. 
A)  It reaches its coldest temperature of 9.76 degrees after 25.76 minutes. 
B)  It reaches its coldest temperature of 25.76 degrees after 9.76 minutes. 
C)  It reaches its coldest temperature of 12.37 degrees after 29.30 minutes. 
D)  It reaches its coldest temperature of 29.30 degrees after 12.37 minutes.

Question 10

What value of x gives a minimum for   ? Restrict your attention to the horizontal span of 9 to 15.Be careful.You are asked about a minimum, not a maximum.Round your answer to two decimal places. ​

Accepted Answer

A)  47.69 
B)  15.00 
C)  37.26 
D)  11.82 
A)  47.69 
B)  15.00 
C)  37.26 
D)  11.82

Question 11

What is the maximum value of   ? Restrict your attention to the horizontal span of 0 to 20.Round your answer to two decimal places. ​

Accepted Answer

A)  39.13 
B)  12.46 
C)  42.72 
D)  11.30 
A)  39.13 
B)  12.46 
C)  42.72 
D)  11.30

Question 12

For what value of x does   reach a minimum? Restrict your attention to the horizontal span of 0 to 11.Round your answer to two decimal places. ​

Accepted Answer

A)  2.42 
B)  4.27 
C)  0.78 
D)  7.33 
A)  2.42 
B)  4.27 
C)  0.78 
D)  7.33

Question 13

What is the maximum value of   ? Restrict your attention to the horizontal span of 0 to 20.Round your answer to two decimal places. ​

Accepted Answer

A)  1.30 
B)  4.58 
C)  0.07 
D)  7.66 
A)  1.30 
B)  4.58 
C)  0.07 
D)  7.66

Question 14

The circulation M, in thousands, of a magazine depends on the time t, in years, since initial publication.The following relationship is valid over the first 7.00 years:   . When did magazine circulation reach a maximum, and what was the maximum circulation? Round your answers to two decimal places.
​

Accepted Answer

A)  The maximum circulation of 4.67 thousand occurred 54.81 years after initial publication. 
B)  The maximum circulation of 54.81 thousand occurred 4.67 years after initial publication. 
C)  The maximum circulation of 2.89 thousand occurred 57.70 years after initial publication. 
D)  The maximum circulation of 57.70 thousand occurred 2.89 years after initial publication. 
A)  The maximum circulation of 4.67 thousand occurred 54.81 years after initial publication. 
B)  The maximum circulation of 54.81 thousand occurred 4.67 years after initial publication. 
C)  The maximum circulation of 2.89 thousand occurred 57.70 years after initial publication. 
D)  The maximum circulation of 57.70 thousand occurred 2.89 years after initial publication.

Question 15

What is the maximum value of   ? Restrict your attention to the horizontal span of 0 to 10.Round your answer to two decimal places, if necessary. ​

Accepted Answer

A)  8 
B)  12.17 
C)  0.83 
D)  15.34 
A)  8 
B)  12.17 
C)  0.83 
D)  15.34

Question 16

Find the minimum value of   .Restrict your attention to the horizontal span of 0 to 10.Round your answer to two decimal places. ​

Accepted Answer

A)  6.83 
B)  0.83 
C)  1.86 
D)  10.47 
A)  6.83 
B)  0.83 
C)  1.86 
D)  10.47

Exam 10: Optimization

What is the minimum value of ? Restrict your attention to the horizontal span of 0 to 10.Round your answer to two decimal places. ​

What is the maximum value of ? Restrict your attention to the horizontal span of 0 to 4.Round your answer to two decimal places. ​

Find the maximum value of .Restrict your attention to the horizontal span of 0 to 10.Round your answer to two decimal places. ​

What value of x gives the maximum value of ? Restrict your attention to the horizontal span of 0 to 10.Round your answer to two decimal places. ​

Assume that the function is increasing on the horizontal span of 2 to 25.Then the maximum value of on this horizontal span is .

What value of x gives a minimum for ? Restrict your attention to the horizontal span of 9 to 15.Be careful.You are asked about a minimum, not a maximum.Round your answer to two decimal places. ​

What is the maximum value of ? Restrict your attention to the horizontal span of 0 to 20.Round your answer to two decimal places. ​

For what value of x does reach a minimum? Restrict your attention to the horizontal span of 0 to 11.Round your answer to two decimal places. ​

What is the maximum value of ? Restrict your attention to the horizontal span of 0 to 20.Round your answer to two decimal places. ​

What is the maximum value of ? Restrict your attention to the horizontal span of 0 to 10.Round your answer to two decimal places, if necessary. ​

Find the minimum value of .Restrict your attention to the horizontal span of 0 to 10.Round your answer to two decimal places. ​

Functions Given by Formulas

Functions Given by TableChas

Functions Given by Graphs

Functions Given by Words

Table and Trends

Graphs

Solving Linear Equations

Solving Nonlinear Equations

Inequalities

The Geometry of Lines

Linear Functions

Modeling Data with Linear Functions

Linear Regression

Systems of Equations

Exponential Growth and Decay

Constant Percentage Change

Modeling Exponential Data

Modeling Nearly Exponential Data

Logarithmic Functions

Logistic Functions

Power Functions

Modeling Data with Power Functions

Combining and Decomposing Functions

Quadratic Functions

Higher Degree Polynomials and Rational Functions

Velocity

Rates of Change for Other Functions

Estimating Rates of Change

Equations of Change Linear and Exponential Functions

Equations of Change Graphical Solutions

Filters

What is the minimum value of ? Restrict your attention to the horizontal span of 0 to 10.Round your answer to two decimal places.

What is the maximum value of ? Restrict your attention to the horizontal span of 0 to 4.Round your answer to two decimal places.

Find the maximum value of .Restrict your attention to the horizontal span of 0 to 10.Round your answer to two decimal places.

What value of x gives the maximum value of ? Restrict your attention to the horizontal span of 0 to 10.Round your answer to two decimal places.

What value of x gives a minimum for ? Restrict your attention to the horizontal span of 9 to 15.Be careful.You are asked about a minimum, not a maximum.Round your answer to two decimal places.

What is the maximum value of ? Restrict your attention to the horizontal span of 0 to 20.Round your answer to two decimal places.

For what value of x does reach a minimum? Restrict your attention to the horizontal span of 0 to 11.Round your answer to two decimal places.

What is the maximum value of ? Restrict your attention to the horizontal span of 0 to 20.Round your answer to two decimal places.

What is the maximum value of ? Restrict your attention to the horizontal span of 0 to 10.Round your answer to two decimal places, if necessary.

Find the minimum value of .Restrict your attention to the horizontal span of 0 to 10.Round your answer to two decimal places.