Question 1

Determine the maximum value of f(x) = -2 $x ^ { 3 }$ + 6x + 3 on 0 ≤ x ≤ 2.
Enter just an integer.

Accepted Answer

The answer of Determine the maximum value of f(x) =...

Question 2

Is this the graph of f(x) = $\frac { 1 } { x + 2 }$ ?

Accepted Answer

A) True 
 B)False

Question 3

The graph of a function f(x) is sketched below. Which of the following is f(x)?

Accepted Answer

A)  f(x) = $\frac { 1 } { x }$ - $x ^ { 2 }$ 
B)  f(x) = $\frac { 1 } { x + 2 }$ - x 
C)  f(x) = - $x ^ { 2 }$ - $x ^ { 3 }$ 
D)  f(x) = $\frac { 1 } { x ^ { 2 } }$ 
A)  f(x) = $\frac { 1 } { x }$ - $x ^ { 2 }$ 
B)  f(x) = $\frac { 1 } { x + 2 }$ - x 
C)  f(x) = - $x ^ { 2 }$ - $x ^ { 3 }$ 
D)  f(x) = $\frac { 1 } { x ^ { 2 } }$

Question 4

Which of the following most resembles the graph of f(x) = $\frac { 1 } { ( 2 - 3 x ) ^ { 3 } }$ near x = $\frac { 2 } { 3 }$ ?

Accepted Answer

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

Question 5

Which of the following is the graph of y = $\frac { 1 } { x }$ + 2x + 5?

Accepted Answer

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

Question 6

Is this the graph of a function having the following properties?
(I) x-intercept at x = -2
(II) absolute maximum at x = -1
(III) relative maximum at x = 1
(IV) concave up for x ≥ 2

Accepted Answer

A) True 
 B)False

Question 7

If the second derivative of a function is $f ^ { \prime \prime } ( x ) = ( x - 2 ) ^ { 2 } \left( x ^ { 2 } - 9 \right)$ is (2, f(2)) an inflection point'

Accepted Answer

A) True 
 B)False

Question 8

What is the maximum area that can be enclosed in a rectangular shape with 100 feet of fence if one of the two long sides is not fenced (there is a natural boundary there)?

Accepted Answer

A)  1000 square feet 
B)  2500 square feet 
C)  625 square feet 
D)  1250 square feet 
E)  none of these 
A)  1000 square feet 
B)  2500 square feet 
C)  625 square feet 
D)  1250 square feet 
E)  none of these

Question 9

What are the x-intercepts of the graph of y = 3 $x ^ { 3 }$ + 24?

Accepted Answer

A)  (24, 0) 
B)  (2, 0) 
C)  (0, -2) 
D)  (0, 24) 
E)  none of these 
A)  (24, 0) 
B)  (2, 0) 
C)  (0, -2) 
D)  (0, 24) 
E)  none of these

Question 10

Suppose that 20,000 fans will go to a ball game when the price of a ticket is $5.00, and that 500 fewer fans will go for each $1.00 increase in ticket price. By how much should ticket prices be increased (or decreased) in order to maximize revenue?

Accepted Answer

A)  increase price by $17.50 
B)  increase price by $45.00 
C)  increase price by $22.50 
D)  decrease price by $1.00 
A)  increase price by $17.50 
B)  increase price by $45.00 
C)  increase price by $22.50 
D)  decrease price by $1.00

Question 11

Which of the following is (are) true of $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } + 3 x ?$ 
(I) f increasing on (1, ?)
(II) (1, 1) is a relative extreme point
(III) (1, 1) is an inflection point
(IV) f is concave up on (-?, 1)

Accepted Answer

A)  II, III, and IV 
B)  I and III 
C)  I, II, and IV 
D)  I, II, and III 
E)  all of these 
A)  II, III, and IV 
B)  I and III 
C)  I, II, and IV 
D)  I, II, and III 
E)  all of these

Question 12

Compute the maximum profit for the profit function $P ( x ) = \frac { x ^ { 3 } } { 3 } - \frac { 9 } { 2 } x ^ { 2 } + 8 x$ Enter your answer as just a real number rounded off to two decimal places (no label).

Accepted Answer

The answer of Compute the maximum profit for the profit...

Question 13

In planning a sidewalk cafe, it is estimated that if there are 28 tables, the daily profit will be $8 per table and that, if the number of tables is increased by x, the profit per table will be reduced by $\frac { 1 } { 4 }$ x dollars (due to overcrowding). How many tables should be present in order to maximize the profit?

Accepted Answer

A)  20 
B)  30 
C)  10 
D)  can't do the problem without cost information 
A)  20 
B)  30 
C)  10 
D)  can't do the problem without cost information

Question 14

Find the x coordinates of all relative extreme points of $f ( x ) = \frac { 1 } { 4 } x ^ { 4 } + \frac { 2 } { 3 } x ^ { 3 } - \frac { 3 } { 2 } x ^ { 2 } + 4$

Accepted Answer

A)  x = -3, 0, 1 
B)  x = -1, 0, 3 
C)  x = -3, 1 
D)  x = 0 
E)  x = -1, 3 
A)  x = -3, 0, 1 
B)  x = -1, 0, 3 
C)  x = -3, 1 
D)  x = 0 
E)  x = -1, 3

Question 15

At which labeled point(s) is the graph concave up?

Accepted Answer

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

Question 16

Suppose a ball is thrown into the air and after t seconds has a height of $h ( t ) = - 16 t ^ { 2 } + 80 t$ feet. When will it reach its maximum height?

Accepted Answer

A)  5 sec 
B)  300 sec 
C)  0.5 sec 
D)  2.5 sec 
E)  none of these 
A)  5 sec 
B)  300 sec 
C)  0.5 sec 
D)  2.5 sec 
E)  none of these

Question 17

Is this the graph of a function having the following properties ?
(I) f(0) = -5
(II) f'(0) = 0
(III) f''(0) = 12
(IV) f( $\sqrt { 7 }$ ) = f(- $\sqrt { 7 }$ ) = -12

Accepted Answer

A) True 
 B)False

Question 18

At which labeled point(s) is the function increasing?

Accepted Answer

A)  A 
B)  A, E 
C)  C, F 
D)  E 
A)  A 
B)  A, E 
C)  C, F 
D)  E

Question 19

A rectangular garden of area 50 square feet is to be surrounded on three sides by a fence costing $2 per running foot and on one side by a brick wall costing $6 per running foot. Let x be the length of the brick wall side. Which of the following represents the total cost of the material?

Accepted Answer

A)  3x + (50 - x) 
B)  6x + $\frac { 50 } { x }$ 
C)  6x + $\frac { 300 } { x }$ 
D)  $\frac { 3 x } { 50 }+ \frac { 1 } { 50 x }$ 
E)  none of these 
A)  3x + (50 - x) 
B)  6x + $\frac { 50 } { x }$ 
C)  6x + $\frac { 300 } { x }$ 
D)  $\frac { 3 x } { 50 }+ \frac { 1 } { 50 x }$ 
E)  none of these

Question 20

Determine the minimum value of f(x) = $\left( x ^ { 2 } - 2 x + 2 \right) ^ { 2 } + 2 \left( x ^ { 2 } - 2 x + 2 \right)$
Enter just an integer.

Accepted Answer

The answer of Determine the minimum value of f(x) =...

Determine the maximum value of f(x) = -2 $x ^ { 3 }$ + 6x + 3 on 0 ≤ x ≤ 2. Enter just an integer.

Is this the graph of f(x) = $\frac { 1 } { x + 2 }$ ? $Is this the graph of f(x) = \frac { 1 } { x + 2 } ?$

The graph of a function f(x) is sketched below. Which of the following is f(x)?

Which of the following most resembles the graph of f(x) = $\frac { 1 } { ( 2 - 3 x ) ^ { 3 } }$ near x = $\frac { 2 } { 3 }$ ?

Which of the following is the graph of y = $\frac { 1 } { x }$ + 2x + 5?

Is this the graph of a function having the following properties? (I) x-intercept at x = -2 (II) absolute maximum at x = -1 (III) relative maximum at x = 1 (IV) concave up for x ≥ 2

If the second derivative of a function is $f ^ { \prime \prime } ( x ) = ( x - 2 ) ^ { 2 } \left( x ^ { 2 } - 9 \right)$ is (2, f(2)) an inflection point'

What is the maximum area that can be enclosed in a rectangular shape with 100 feet of fence if one of the two long sides is not fenced (there is a natural boundary there)?

What are the x-intercepts of the graph of y = 3 $x ^ { 3 }$ + 24?

Suppose that 20,000 fans will go to a ball game when the price of a ticket is $5.00, and that 500 fewer fans will go for each $1.00 increase in ticket price. By how much should ticket prices be increased (or decreased) in order to maximize revenue?

Which of the following is (are) true of $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } + 3 x ?$ (I) f increasing on (1, ?) (II) (1, 1) is a relative extreme point (III) (1, 1) is an inflection point (IV) f is concave up on (-?, 1)

Compute the maximum profit for the profit function $P ( x ) = \frac { x ^ { 3 } } { 3 } - \frac { 9 } { 2 } x ^ { 2 } + 8 x$ Enter your answer as just a real number rounded off to two decimal places (no label).

Find the x coordinates of all relative extreme points of $f ( x ) = \frac { 1 } { 4 } x ^ { 4 } + \frac { 2 } { 3 } x ^ { 3 } - \frac { 3 } { 2 } x ^ { 2 } + 4$

At which labeled point(s) is the graph concave up?

Suppose a ball is thrown into the air and after t seconds has a height of $h ( t ) = - 16 t ^ { 2 } + 80 t$ feet. When will it reach its maximum height?

At which labeled point(s) is the function increasing?

A rectangular garden of area 50 square feet is to be surrounded on three sides by a fence costing $2 per running foot and on one side by a brick wall costing $6 per running foot. Let x be the length of the brick wall side. Which of the following represents the total cost of the material?

Determine the minimum value of f(x) = $\left( x ^ { 2 } - 2 x + 2 \right) ^ { 2 } + 2 \left( x ^ { 2 } - 2 x + 2 \right)$ Enter just an integer.

The Derivative

Techniques of Differentiation

Logarithm Functions

Applications of the Exponential and Natural Logarithm Functions

The Definite Integral

Functions of Several Variables

The Trigonometric Functions

Techniques of Integration

Differential Equations

Taylor Polynomials and Infinite Series

Probability and Calculus

Filters

Exam 2: Applications of the Derivative

Determine the maximum value of f(x) = -2 x3x ^ { 3 }x3 + 6x + 3 on 0 ≤ x ≤ 2. Enter just an integer.

Is this the graph of f(x) = 1x+2\frac { 1 } { x + 2 }x+21​ ?

The graph of a function f(x) is sketched below. Which of the following is f(x)?

Which of the following most resembles the graph of f(x) = 1(2−3x)3\frac { 1 } { ( 2 - 3 x ) ^ { 3 } }(2−3x)31​ near x = 23\frac { 2 } { 3 }32​ ?

Which of the following is the graph of y = 1x\frac { 1 } { x }x1​ + 2x + 5?

Is this the graph of a function having the following properties? (I) x-intercept at x = -2 (II) absolute maximum at x = -1 (III) relative maximum at x = 1 (IV) concave up for x ≥ 2

If the second derivative of a function is f′′(x)=(x−2)2(x2−9)f ^ { \prime \prime } ( x ) = ( x - 2 ) ^ { 2 } \left( x ^ { 2 } - 9 \right)f′′(x)=(x−2)2(x2−9) is (2, f(2)) an inflection point'

What is the maximum area that can be enclosed in a rectangular shape with 100 feet of fence if one of the two long sides is not fenced (there is a natural boundary there)?

What are the x-intercepts of the graph of y = 3 x3x ^ { 3 }x3 + 24?

Suppose that 20,000 fans will go to a ball game when the price of a ticket is $5.00, and that 500 fewer fans will go for each $1.00 increase in ticket price. By how much should ticket prices be increased (or decreased) in order to maximize revenue?

Which of the following is (are) true of f(x)=x3−3x2+3x?f ( x ) = x ^ { 3 } - 3 x ^ { 2 } + 3 x ?f(x)=x3−3x2+3x? (I) f increasing on (1, ?) (II) (1, 1) is a relative extreme point (III) (1, 1) is an inflection point (IV) f is concave up on (-?, 1)

Compute the maximum profit for the profit function P(x)=x33−92x2+8xP ( x ) = \frac { x ^ { 3 } } { 3 } - \frac { 9 } { 2 } x ^ { 2 } + 8 xP(x)=3x3​−29​x2+8x Enter your answer as just a real number rounded off to two decimal places (no label).

Find the x coordinates of all relative extreme points of f(x)=14x4+23x3−32x2+4f ( x ) = \frac { 1 } { 4 } x ^ { 4 } + \frac { 2 } { 3 } x ^ { 3 } - \frac { 3 } { 2 } x ^ { 2 } + 4f(x)=41​x4+32​x3−23​x2+4

At which labeled point(s) is the graph concave up?

Suppose a ball is thrown into the air and after t seconds has a height of h(t)=−16t2+80th ( t ) = - 16 t ^ { 2 } + 80 th(t)=−16t2+80t feet. When will it reach its maximum height?

Is this the graph of a function having the following properties ? (I) f(0) = -5 (II) f'(0) = 0 (III) f''(0) = 12 (IV) f( 7\sqrt { 7 }7​ ) = f(- 7\sqrt { 7 }7​ ) = -12

At which labeled point(s) is the function increasing?

A rectangular garden of area 50 square feet is to be surrounded on three sides by a fence costing $2 per running foot and on one side by a brick wall costing $6 per running foot. Let x be the length of the brick wall side. Which of the following represents the total cost of the material?

Determine the minimum value of f(x) = (x2−2x+2)2+2(x2−2x+2)\left( x ^ { 2 } - 2 x + 2 \right) ^ { 2 } + 2 \left( x ^ { 2 } - 2 x + 2 \right)(x2−2x+2)2+2(x2−2x+2) Enter just an integer.

The Derivative

Techniques of Differentiation

Logarithm Functions

Applications of the Exponential and Natural Logarithm Functions

The Definite Integral

Functions of Several Variables

The Trigonometric Functions

Techniques of Integration

Differential Equations

Taylor Polynomials and Infinite Series

Probability and Calculus

Filters

Determine the maximum value of f(x) = -2 $x ^ { 3 }$ + 6x + 3 on 0 ≤ x ≤ 2. Enter just an integer.

Is this the graph of f(x) = $\frac { 1 } { x + 2 }$ ? $Is this the graph of f(x) = \frac { 1 } { x + 2 } ?$

Which of the following most resembles the graph of f(x) = $\frac { 1 } { ( 2 - 3 x ) ^ { 3 } }$ near x = $\frac { 2 } { 3 }$ ?

Which of the following is the graph of y = $\frac { 1 } { x }$ + 2x + 5?

If the second derivative of a function is $f ^ { \prime \prime } ( x ) = ( x - 2 ) ^ { 2 } \left( x ^ { 2 } - 9 \right)$ is (2, f(2)) an inflection point'

What are the x-intercepts of the graph of y = 3 $x ^ { 3 }$ + 24?

Which of the following is (are) true of $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } + 3 x ?$ (I) f increasing on (1, ?) (II) (1, 1) is a relative extreme point (III) (1, 1) is an inflection point (IV) f is concave up on (-?, 1)

Compute the maximum profit for the profit function $P ( x ) = \frac { x ^ { 3 } } { 3 } - \frac { 9 } { 2 } x ^ { 2 } + 8 x$ Enter your answer as just a real number rounded off to two decimal places (no label).

Find the x coordinates of all relative extreme points of $f ( x ) = \frac { 1 } { 4 } x ^ { 4 } + \frac { 2 } { 3 } x ^ { 3 } - \frac { 3 } { 2 } x ^ { 2 } + 4$

Suppose a ball is thrown into the air and after t seconds has a height of $h ( t ) = - 16 t ^ { 2 } + 80 t$ feet. When will it reach its maximum height?

Determine the minimum value of f(x) = $\left( x ^ { 2 } - 2 x + 2 \right) ^ { 2 } + 2 \left( x ^ { 2 } - 2 x + 2 \right)$ Enter just an integer.