Question 1

Determine all critical points for the function.
-f(x) =   + 6x + 9

Accepted Answer

A)  x = 3 
B)  x = 0 
C)  x = -6 
D)  x = -3 
A)  x = 3 
B)  x = 0 
C)  x = -6 
D)  x = -3

Question 2

Graph the equation. Include the coordinates of any local extreme points and inflection points.
-y = x

Accepted Answer

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

Question 3

Determine all critical points for the function.
-f(x) =   - 12x - 5

Accepted Answer

A)  x = -2 
B)  x = -2 and x = 2 
C)  x = 2 
D)  x = -2, x = 0, and x = 2 
A)  x = -2 
B)  x = -2 and x = 2 
C)  x = 2 
D)  x = -2, x = 0, and x = 2

Question 4

Find the absolute extreme values of the function on the interval.
-f(x) = ln(x + 2) +   , 1 $\le$ x $\le$ 5

Accepted Answer

A)  absolute minimum value is ln 4 + 1/2 at x = 2; absolute maximum value is ln 3 + 1 at x = 1 
B)  absolute minimum value is ln 4 + 1/2 at x = 2; absolute maximum value is ln 7 + 1/5 at x = 5 
C)  absolute minimum value is ln 3 + 1 at x = 1; absolute maximum value is ln 7 + 1/5 at x = 5 
D)  absolute minimum value is -1 at x = -1; absolute maximum value is ln 7 + 1/5 at x = 5 
A)  absolute minimum value is ln 4 + 1/2 at x = 2; absolute maximum value is ln 3 + 1 at x = 1 
B)  absolute minimum value is ln 4 + 1/2 at x = 2; absolute maximum value is ln 7 + 1/5 at x = 5 
C)  absolute minimum value is ln 3 + 1 at x = 1; absolute maximum value is ln 7 + 1/5 at x = 5 
D)  absolute minimum value is -1 at x = -1; absolute maximum value is ln 7 + 1/5 at x = 5

Question 5

Find the most general antiderivative.      
-  dy

Accepted Answer

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

Question 6

Choose the one alternative that best completes the statement or answers the question. 
-Find the optimum number of batches (to the nearest whole number) of an item that should be produced annually (in order to minimize cost) if 50,000 units are to be made, it costs $ 4 to store a unit for one year, and it costs $ 500 to set up the factory to produce each batch. Assume that units of this item will be sold off throughout the year, so the cost equation will use the average cost.

Accepted Answer

A)  10 batches 
B)  12 batches 
C)  14 batches 
D)  16 batches 
A)  10 batches 
B)  12 batches 
C)  14 batches 
D)  16 batches

Question 7

Solve the problem.
-The graphs below show the first and second derivatives of a function   . Select a possible graph of f that passes through point P.

Accepted Answer

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

Question 8

Use l'Hopital's Rule to evaluate the limit.
-

Accepted Answer

A)  -16 
B)  -8 
C)  16 
D)  8 
A)  -16 
B)  -8 
C)  16 
D)  8

Question 9

Use differentiation to determine whether the integral formula is correct.
-

Accepted Answer

A) True 
 B)False

Question 10

Choose the one alternative that best completes the statement or answers the question. 
-A private shipping company will accept a box for domestic shipment only if the sum of its length and girth (distance around) does not exceed 114 in. Suppose you want to mail a box with square sides so that its dimensions are   and it's girth is   What dimensions will give the box its largest volume?

Accepted Answer

A)  38 in. × 19 in. × 38 in. 
B)  19 in. × 19 in. × 38 in. 
C)  19 in. × 19 in. × 95 in. 
D)  76/3 in. × 76/3 in. × 19 in. 
A)  38 in. × 19 in. × 38 in. 
B)  19 in. × 19 in. × 38 in. 
C)  19 in. × 19 in. × 95 in. 
D)  76/3 in. × 76/3 in. × 19 in.

Question 11

Solve the initial value problem. 
-  =   ;   = 4, r(1) = 5

Accepted Answer

A)  r = 3/t + 7t - 5 
B)  r = 3/t + 7t + 15 
C)  r = 3t + 7t + 15 
D)  r =   +   t - 5 
A)  r = 3/t + 7t - 5 
B)  r = 3/t + 7t + 15 
C)  r = 3t + 7t + 15 
D)  r =   +   t - 5

Question 12

Find the largest open interval where the function is changing as requested.
-Increasing y = (x2 - 9)2

Accepted Answer

A)  (-3, 0) 
B)  (-$\infty$, 0) 
C)  (-3, 3) 
D)  (3, $\infty$) 
A)  (-3, 0) 
B)  (-$\infty$, 0) 
C)  (-3, 3) 
D)  (3, $\infty$)

Question 13

Solve the problem.
-The graphs below show the first and second derivatives of a function   . Select a possible graph f that passes through the point P.

Accepted Answer

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

Question 14

Graph the equation. Include the coordinates of any local extreme points and inflection points.
-y = x + cos 2x, 0 $\le$x $\le$ $\infty$

Accepted Answer

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

Question 15

Solve the problem. 
-Given the velocity and initial position of a body moving along a coordinate line at time t, find the body's position at time t. v =   sin   , s(   ) = 2

Accepted Answer

A)  s = -2 cos   + 4 
B)  s = -2 cos   + 3.3073 
C) s = -2 cos   + 8.2134 
D)  s = 2 cos   + 4 
A)  s = -2 cos   + 4 
B)  s = -2 cos   + 3.3073 
C) s = -2 cos   + 8.2134 
D)  s = 2 cos   + 4

Question 16

Solve the problem.
-The graphs below show the first and second derivatives of a function   . Select a possible graph f that passes through the point P.

Accepted Answer

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

Question 17

Use differentiation to determine whether the integral formula is correct.
-

Accepted Answer

A) True 
 B)False

Question 18

Provide an appropriate response.  
-

Accepted Answer

A)  -5.3 
B)  184.5 
C)  200.5 
D)  Not enough information is given. 
A)  -5.3 
B)  184.5 
C)  200.5 
D)  Not enough information is given.

Question 19

L'Hopital's rule does not help with the given limit. Find the limit some other way.
-

Accepted Answer

A)  1 
B)  $\infty$ 
C)  -1 
D)  0 
A)  1 
B)  $\infty$ 
C)  -1 
D)  0

Question 20

Use l'Hopital's Rule to evaluate the limit.
-

Accepted Answer

A)  -5 
B)  0 
C)  1 
D)  5 
A)  -5 
B)  0 
C)  1 
D)  5

Determine all critical points for the function. -f(x) = + 6x + 9

Graph the equation. Include the coordinates of any local extreme points and inflection points. -y = x

Determine all critical points for the function. -f(x) = - 12x - 5

Find the absolute extreme values of the function on the interval. -f(x) = ln(x + 2) + $Find the absolute extreme values of the function on the interval. -f(x) = ln(x + 2) + , 1 \le x \le 5$ , 1 $\le$ x $\le$ 5

Find the most general antiderivative. - dy

Solve the problem. -The graphs below show the first and second derivatives of a function . Select a possible graph of f that passes through point P.

Use l'Hopital's Rule to evaluate the limit. -

Use differentiation to determine whether the integral formula is correct. -

Solve the initial value problem. - = ; = 4, r(1) = 5

Find the largest open interval where the function is changing as requested. -Increasing y = (x² - 9)²

Solve the problem. -The graphs below show the first and second derivatives of a function . Select a possible graph f that passes through the point P.

Graph the equation. Include the coordinates of any local extreme points and inflection points. -y = x + cos 2x, 0 $\le$ x $\le$ $\infty$ $Graph the equation. Include the coordinates of any local extreme points and inflection points. -y = x + cos 2x, 0 \le x \le \infty$

Solve the problem. -Given the velocity and initial position of a body moving along a coordinate line at time t, find the body's position at time t. v = sin , s( ) = 2

Solve the problem. -The graphs below show the first and second derivatives of a function . Select a possible graph f that passes through the point P.

Use differentiation to determine whether the integral formula is correct. -

Provide an appropriate response. -

L'Hopital's rule does not help with the given limit. Find the limit some other way. -

Use l'Hopital's Rule to evaluate the limit. -

Functions

Limits

Derivatives

Integration

Applications of Integration

Logarithmic, Exponential, and Hyperbolic Functions

Integration Techniques

Differential Equations

Sequences and Infinite Series

Power Series

Parametric and Polar Curves

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Calculus

Filters

Exam 4: Applications of the Derivative

Determine all critical points for the function. -f(x) = + 6x + 9

Graph the equation. Include the coordinates of any local extreme points and inflection points. -y = x

Determine all critical points for the function. -f(x) = - 12x - 5

Find the absolute extreme values of the function on the interval. -f(x) = ln(x + 2) + , 1 ≤\le≤ x ≤\le≤ 5

Find the most general antiderivative. - dy

Solve the problem. -The graphs below show the first and second derivatives of a function . Select a possible graph of f that passes through point P.

Use l'Hopital's Rule to evaluate the limit. -

Use differentiation to determine whether the integral formula is correct. -

Solve the initial value problem. - = ; = 4, r(1) = 5

Find the largest open interval where the function is changing as requested. -Increasing y = (x2 - 9)2

Solve the problem. -The graphs below show the first and second derivatives of a function . Select a possible graph f that passes through the point P.

Graph the equation. Include the coordinates of any local extreme points and inflection points. -y = x + cos 2x, 0 ≤\le≤ x ≤\le≤ ∞\infty∞

Solve the problem. -Given the velocity and initial position of a body moving along a coordinate line at time t, find the body's position at time t. v = sin , s( ) = 2

Solve the problem. -The graphs below show the first and second derivatives of a function . Select a possible graph f that passes through the point P.

Use differentiation to determine whether the integral formula is correct. -

Provide an appropriate response. -

L'Hopital's rule does not help with the given limit. Find the limit some other way. -

Use l'Hopital's Rule to evaluate the limit. -

Functions

Limits

Derivatives

Integration

Applications of Integration

Logarithmic, Exponential, and Hyperbolic Functions

Integration Techniques

Differential Equations

Sequences and Infinite Series

Power Series

Parametric and Polar Curves

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Calculus

Filters

Find the absolute extreme values of the function on the interval. -f(x) = ln(x + 2) + $Find the absolute extreme values of the function on the interval. -f(x) = ln(x + 2) + , 1 \le x \le 5$ , 1 $\le$ x $\le$ 5

Find the largest open interval where the function is changing as requested. -Increasing y = (x² - 9)²

Graph the equation. Include the coordinates of any local extreme points and inflection points. -y = x + cos 2x, 0 $\le$ x $\le$ $\infty$ $Graph the equation. Include the coordinates of any local extreme points and inflection points. -y = x + cos 2x, 0 \le x \le \infty$