Question 1

The graph of $f ( x ) = 2 x ^ { 3 } - 3 x ^ { 2 } - 12 x - 5$ is concave down for $x < \frac { 1 } { 2 }$ .

Accepted Answer

A) True 
 B)False  True

Question 2

Find all vertical and horizontal asymptotes of the graph of the given function. $f ( x ) = \frac { x ^ { 2 } - 5 x } { x ^ { 2 } - x - 6 }$

Accepted Answer

Vertical asymptotes: x = -2, x = 3; horizontal asymptote: y = 1

Question 3

The graph of $g ( t ) = t ^ { 4 } + 2 t ^ { 3 }$ is concave up everywhere.

Accepted Answer

A) True 
 B)False  False

Question 4

A company that distributes landscape materials buys 4,000 tons of pine mulch a year. The ordering fee is $30 per shipment, the mulch costs them $20 per ton, and annual storage costs are $1.50 per ton. How many tons should be ordered in each shipment to minimize the total annual cost?

Accepted Answer

A)  2,000 tons 
B)  400 tons 
C)  200 tons 
D)  500 tons 
A)  2,000 tons 
B)  400 tons 
C)  200 tons 
D)  500 tons

Question 5

Find the absolute maximum and minimum of $f ( x ) = x ^ { 4 } - 8 x ^ { 2 } + 12$ on the interval -1 $\le$ x $\le$ 2.

Accepted Answer

Maximum is

Question 6

Find all critical numbers of the function $f ( x ) = \frac { x - 1 } { x ^ { 2 } + 3 }$ .

Accepted Answer

The answer of Find all critical numbers of the function...

Question 7

Graph $f ( x ) = x ^ { 2 } + 4 x + 5$ .

Accepted Answer

@#IMG-DLM& (Each tic

Question 8

Find two non-negative numbers whose sum is 16 for which the product of their squares is as large as possible.

Accepted Answer

A)  8 and 8 
B)  0 and 16 
C)  1 and 15 
D)  6 and 10 
A)  8 and 8 
B)  0 and 16 
C)  1 and 15 
D)  6 and 10

Question 9

A 5-year projection of population trends suggests that t years from now, the population of a certain community will be $P ( t ) = - t ^ { 3 } + 12 t ^ { 2 } + 144 t + 50$ thousand.
a. At what time during the 5-year period will the population be growing most rapidly?
b. At what time during the 5-year period will the population be growing least rapidly?
c. At what time is the rate of population growth changing most rapidly?

Accepted Answer

a. t = 4 y

Question 10

Sketch the graph of the given function. $$f ( x ) = \frac { x - 3 } { x + 1 }$$

Accepted Answer

The answer of Sketch the graph of the given function....

Question 11

Find all intervals where the derivative of the function shown below is negative.

Accepted Answer

-5 < x < 0

Question 12

A manufacturer estimates that if he produces x units of a particular commodity, the total cost will be $C ( x ) = x ^ { 3 } - 24 x ^ { 2 } + 350 x + 400$ dollars. For what value of x does the marginal cost $M ( x ) = C ^ { t } ( x )$ satisfy $M ^ { \prime } ( x ) = 0$ ?

Accepted Answer

The answer of A manufacturer estimates that if he produces...

Question 13

Use the second derivative test to find the relative maxima and minima of the function $$f ( x ) = 2 x ^ { 3 } + 6 x ^ { 2 } - 18 x + 1$$ .

Accepted Answer

A)  Relative maximum at (-3, -8); relative minimum at (1, 55) 
B)  Relative maximum at (-3, 55); relative minimum at (1, -9) 
C)  Relative maximum at (-3, -9); relative minimum at (-1, 23) 
D)  Relative maximum at (1, 55); relative minimum at (-3, -9) 
A)  Relative maximum at (-3, -8); relative minimum at (1, 55) 
B)  Relative maximum at (-3, 55); relative minimum at (1, -9) 
C)  Relative maximum at (-3, -9); relative minimum at (-1, 23) 
D)  Relative maximum at (1, 55); relative minimum at (-3, -9)

Question 14

Find the elasticity n of the demand function $D ( p ) = \frac { 3 } { 1 + 2 p ^ { 2 } }$ .

Accepted Answer

The answer of Find the elasticity n of the demand...

Question 15

Find the intervals of increase and decrease for the function $f ( x ) = x ^ { 2 } + 9 x - 4$ .

Accepted Answer

A)  $\text { Decreasing for } x > - \frac { 9 } { 2 } \text { and increasing for } x  - \frac { 9 } { 2 }$ 
C)  Decreasing for all x 
D)  Increasing for all x 
A)  $\text { Decreasing for } x > - \frac { 9 } { 2 } \text { and increasing for } x  - \frac { 9 } { 2 }$ 
C)  Decreasing for all x 
D)  Increasing for all x

Question 16

Sketch the graph of the given function. $$f ( x ) = \frac { x + 5 } { x + 2 }$$

Accepted Answer

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

Question 17

Suppose the total cost of producing x units of a certain commodity is $C ( x ) = 2 x ^ { 4 } - 10 x ^ { 3 } - 18 x ^ { 2 } + 200 x + 167$ . Determine the largest and smallest values of the marginal cost for 0 $\le$ x $\le$ 5.

Accepted Answer

Maximum is

Question 18

The total cost of producing x units of a certain commodity is $C ( x ) = x ^ { 3 } - 5 x ^ { 2 } + 8 x$ . Determine the minimum average cost of the commodity.

Accepted Answer

The answer of The total cost of producing x units...

Question 19

Name the vertical and horizontal asymptotes of the given graph.

Accepted Answer

A)  Vertical asymptotes: x = -4, x = 1; horizontal asymptote: y = 2 
B)  Vertical asymptotes: x = -4, x = 1; horizontal asymptotes: y = 2, y = 0 
C)  Vertical asymptotes: x = -4, x = 1, x = 0; horizontal asymptote: y = 2 
D)  Vertical asymptotes: x = -4, x = 1, x = 0; horizontal asymptotes: y = 2, y = 0 
A)  Vertical asymptotes: x = -4, x = 1; horizontal asymptote: y = 2 
B)  Vertical asymptotes: x = -4, x = 1; horizontal asymptotes: y = 2, y = 0 
C)  Vertical asymptotes: x = -4, x = 1, x = 0; horizontal asymptote: y = 2 
D)  Vertical asymptotes: x = -4, x = 1, x = 0; horizontal asymptotes: y = 2, y = 0

Question 20

Find all the critical numbers of the function. $f ( x ) = 4 x ^ { 2 } - 3 x + 1$

Accepted Answer

A)  -1 
B)  $\frac { 3 } { 8 }$ 
C)  $- \frac { 1 } { 4 }$ 
D)  None 
A)  -1 
B)  $\frac { 3 } { 8 }$ 
C)  $- \frac { 1 } { 4 }$ 
D)  None

The graph of $f ( x ) = 2 x ^ { 3 } - 3 x ^ { 2 } - 12 x - 5$ is concave down for $x < \frac { 1 } { 2 }$ .

Find all vertical and horizontal asymptotes of the graph of the given function. $f ( x ) = \frac { x ^ { 2 } - 5 x } { x ^ { 2 } - x - 6 }$

The graph of $g ( t ) = t ^ { 4 } + 2 t ^ { 3 }$ is concave up everywhere.

A company that distributes landscape materials buys 4,000 tons of pine mulch a year. The ordering fee is $30 per shipment, the mulch costs them $20 per ton, and annual storage costs are $1.50 per ton. How many tons should be ordered in each shipment to minimize the total annual cost?

Find the absolute maximum and minimum of $f ( x ) = x ^ { 4 } - 8 x ^ { 2 } + 12$ on the interval -1 $\le$ x $\le$ 2.

Find all critical numbers of the function $f ( x ) = \frac { x - 1 } { x ^ { 2 } + 3 }$ .

Graph $f ( x ) = x ^ { 2 } + 4 x + 5$ .

Find two non-negative numbers whose sum is 16 for which the product of their squares is as large as possible.

Sketch the graph of the given function. $f ( x ) = \frac { x - 3 } { x + 1 }$

Find all intervals where the derivative of the function shown below is negative.

A manufacturer estimates that if he produces x units of a particular commodity, the total cost will be $C ( x ) = x ^ { 3 } - 24 x ^ { 2 } + 350 x + 400$ dollars. For what value of x does the marginal cost $M ( x ) = C ^ { t } ( x )$ satisfy $M ^ { \prime } ( x ) = 0$ ?

Use the second derivative test to find the relative maxima and minima of the function $f ( x ) = 2 x ^ { 3 } + 6 x ^ { 2 } - 18 x + 1$ .

Find the elasticity n of the demand function $D ( p ) = \frac { 3 } { 1 + 2 p ^ { 2 } }$ .

Find the intervals of increase and decrease for the function $f ( x ) = x ^ { 2 } + 9 x - 4$ .

Sketch the graph of the given function. $f ( x ) = \frac { x + 5 } { x + 2 }$

Suppose the total cost of producing x units of a certain commodity is $C ( x ) = 2 x ^ { 4 } - 10 x ^ { 3 } - 18 x ^ { 2 } + 200 x + 167$ . Determine the largest and smallest values of the marginal cost for 0 $\le$ x $\le$ 5.

The total cost of producing x units of a certain commodity is $C ( x ) = x ^ { 3 } - 5 x ^ { 2 } + 8 x$ . Determine the minimum average cost of the commodity.

Name the vertical and horizontal asymptotes of the given graph.

Find all the critical numbers of the function. $f ( x ) = 4 x ^ { 2 } - 3 x + 1$

Functions, Graphs, and Limits

Differentiation: Basic Concepts

Exponential and Logarithmic Functions

Integration

Additional Topics in Integration

Calculus of Several Variables

Appendix: Algebra Review

Filters

Exam 3: Additional Applications of the Derivative

The graph of f(x)=2x3−3x2−12x−5f ( x ) = 2 x ^ { 3 } - 3 x ^ { 2 } - 12 x - 5f(x)=2x3−3x2−12x−5 is concave down for x<12x < \frac { 1 } { 2 }x<21​ .

Find all vertical and horizontal asymptotes of the graph of the given function. f(x)=x2−5xx2−x−6f ( x ) = \frac { x ^ { 2 } - 5 x } { x ^ { 2 } - x - 6 }f(x)=x2−x−6x2−5x​

The graph of g(t)=t4+2t3g ( t ) = t ^ { 4 } + 2 t ^ { 3 }g(t)=t4+2t3 is concave up everywhere.

A company that distributes landscape materials buys 4,000 tons of pine mulch a year. The ordering fee is $30 per shipment, the mulch costs them $20 per ton, and annual storage costs are $1.50 per ton. How many tons should be ordered in each shipment to minimize the total annual cost?

Find the absolute maximum and minimum of f(x)=x4−8x2+12f ( x ) = x ^ { 4 } - 8 x ^ { 2 } + 12f(x)=x4−8x2+12 on the interval -1 ≤\le≤ x ≤\le≤ 2.

Find all critical numbers of the function f(x)=x−1x2+3f ( x ) = \frac { x - 1 } { x ^ { 2 } + 3 }f(x)=x2+3x−1​ .

Graph f(x)=x2+4x+5f ( x ) = x ^ { 2 } + 4 x + 5f(x)=x2+4x+5 .

Find two non-negative numbers whose sum is 16 for which the product of their squares is as large as possible.

Sketch the graph of the given function. f(x)=x−3x+1f ( x ) = \frac { x - 3 } { x + 1 }f(x)=x+1x−3​

Find all intervals where the derivative of the function shown below is negative.

Use the second derivative test to find the relative maxima and minima of the function f(x)=2x3+6x2−18x+1f ( x ) = 2 x ^ { 3 } + 6 x ^ { 2 } - 18 x + 1f(x)=2x3+6x2−18x+1 .

Find the elasticity n of the demand function D(p)=31+2p2D ( p ) = \frac { 3 } { 1 + 2 p ^ { 2 } }D(p)=1+2p23​ .

Find the intervals of increase and decrease for the function f(x)=x2+9x−4f ( x ) = x ^ { 2 } + 9 x - 4f(x)=x2+9x−4 .

Sketch the graph of the given function. f(x)=x+5x+2f ( x ) = \frac { x + 5 } { x + 2 }f(x)=x+2x+5​

Suppose the total cost of producing x units of a certain commodity is C(x)=2x4−10x3−18x2+200x+167C ( x ) = 2 x ^ { 4 } - 10 x ^ { 3 } - 18 x ^ { 2 } + 200 x + 167C(x)=2x4−10x3−18x2+200x+167 . Determine the largest and smallest values of the marginal cost for 0 ≤\le≤ x ≤\le≤ 5.

The total cost of producing x units of a certain commodity is C(x)=x3−5x2+8xC ( x ) = x ^ { 3 } - 5 x ^ { 2 } + 8 xC(x)=x3−5x2+8x . Determine the minimum average cost of the commodity.

Name the vertical and horizontal asymptotes of the given graph.

Find all the critical numbers of the function. f(x)=4x2−3x+1f ( x ) = 4 x ^ { 2 } - 3 x + 1f(x)=4x2−3x+1

Functions, Graphs, and Limits

Differentiation: Basic Concepts

Exponential and Logarithmic Functions

Integration

Additional Topics in Integration

Calculus of Several Variables

Appendix: Algebra Review

Filters

The graph of $f ( x ) = 2 x ^ { 3 } - 3 x ^ { 2 } - 12 x - 5$ is concave down for $x < \frac { 1 } { 2 }$ .

Find all vertical and horizontal asymptotes of the graph of the given function. $f ( x ) = \frac { x ^ { 2 } - 5 x } { x ^ { 2 } - x - 6 }$

The graph of $g ( t ) = t ^ { 4 } + 2 t ^ { 3 }$ is concave up everywhere.

Find the absolute maximum and minimum of $f ( x ) = x ^ { 4 } - 8 x ^ { 2 } + 12$ on the interval -1 $\le$ x $\le$ 2.

Find all critical numbers of the function $f ( x ) = \frac { x - 1 } { x ^ { 2 } + 3 }$ .

Graph $f ( x ) = x ^ { 2 } + 4 x + 5$ .

Sketch the graph of the given function. $f ( x ) = \frac { x - 3 } { x + 1 }$

Use the second derivative test to find the relative maxima and minima of the function $f ( x ) = 2 x ^ { 3 } + 6 x ^ { 2 } - 18 x + 1$ .

Find the elasticity n of the demand function $D ( p ) = \frac { 3 } { 1 + 2 p ^ { 2 } }$ .

Find the intervals of increase and decrease for the function $f ( x ) = x ^ { 2 } + 9 x - 4$ .

Sketch the graph of the given function. $f ( x ) = \frac { x + 5 } { x + 2 }$

Suppose the total cost of producing x units of a certain commodity is $C ( x ) = 2 x ^ { 4 } - 10 x ^ { 3 } - 18 x ^ { 2 } + 200 x + 167$ . Determine the largest and smallest values of the marginal cost for 0 $\le$ x $\le$ 5.

The total cost of producing x units of a certain commodity is $C ( x ) = x ^ { 3 } - 5 x ^ { 2 } + 8 x$ . Determine the minimum average cost of the commodity.

Find all the critical numbers of the function. $f ( x ) = 4 x ^ { 2 } - 3 x + 1$