Question 1

Determine the relative maximum point of $f ( x ) = x ^ { 3 } - 6 x ^ { 2 } + 9 x - 3$ Enter your answer as exactly just an ordered pair of integers: (a, b)

Accepted Answer

(1,1)

Question 2

A manufacturer estimates that the profit from producing x units of a commodity is $- x ^ { 2 } + 40 x - 100$ dollars per week. What is the maximum profit he can realize in one week?

Accepted Answer

A)  $300 
B)  $275 
C)  $500 
D)  $400 
E)  none of these 
A)  $300 
B)  $275 
C)  $500 
D)  $400 
E)  none of these A

Question 3

Find the relative minimum point(s) of $f ( x ) = \frac { x ^ { 4 } } { 4 } - x ^ { 3 } - 5 x ^ { 2 } - 10$

Accepted Answer

A)  (-2, f(-2)) and (0, f(0)) 
B)  (2, f(2)) and (-5, f(-5)) 
C)  (-2, f(-2)) and (5, f(5)) 
D)  (0, f(0)) 
E)  none of these 
A)  (-2, f(-2)) and (0, f(0)) 
B)  (2, f(2)) and (-5, f(-5)) 
C)  (-2, f(-2)) and (5, f(5)) 
D)  (0, f(0)) 
E)  none of these C

Question 4

Find the inflection point(s) of $f ( x ) = \frac { 2 } { 3 } x ^ { 3 } - 7 x ^ { 2 } + 24 x - 16$.

Accepted Answer

A)  $\left( \frac { 7 } { 2 } , \mathrm { f } \left( \frac { 7 } { 2 } \right) \right.$ 
B)  (2, f (2)) and (6, f (6)) 
C)  (56, f (56)) 
D)  (3, f (3)) and (4, f (4)) 
E)  $\left( \frac { 2 } { 7 } , \mathrm { f } \left( \frac { 2 } { 7 } \right) \right.$ 
A)  $\left( \frac { 7 } { 2 } , \mathrm { f } \left( \frac { 7 } { 2 } \right) \right.$ 
B)  (2, f (2)) and (6, f (6)) 
C)  (56, f (56)) 
D)  (3, f (3)) and (4, f (4)) 
E)  $\left( \frac { 2 } { 7 } , \mathrm { f } \left( \frac { 2 } { 7 } \right) \right.$

Question 5

This is the graph of f(x) = $\frac { 1 } { 3 }$ $x ^ { 3 }$ - $\frac { 1 } { 2 }$ $x ^ { 2 }$ - 6x. What is the inflection point?
Enter your answer exactly as just an ordered pair of reduced fractions of form $\frac { a } { b }$ , or integers (a, b), or the word "none".

Accepted Answer

The answer of This is the graph of f(x) =...

Question 6

Find the x coordinates of all relative extreme points of $f ( x ) = \frac { 2 } { 3 } x ^ { 3 } - 7 x ^ { 2 } + 24 x - 72$

Accepted Answer

A)  x = 2, 6 
B)  x = -4, -3, 0 
C)  x = 3, 4 
D)  x = 0, 3, 4 
E)  x = -4, -3 
A)  x = 2, 6 
B)  x = -4, -3, 0 
C)  x = 3, 4 
D)  x = 0, 3, 4 
E)  x = -4, -3

Question 7

Is this the graph of a function having the following properties?
(I) f'(x)  0 for all x < 0
(III) (0, 1) is a point on the graph

Accepted Answer

A) True 
 B)False

Question 8

Find the relative extreme points for $f ( x ) = x ^ { 3 } + 6 x ^ { 2 } - 15 x$

Accepted Answer

A)  (5, f(5)) is a relative extreme minimum point, (-1, f(-1)) a relative extreme maximum 
B)  (0, f(0)) is a relative extreme minimum point 
C)  (5, f(5)) is a relative extreme maximum point, (-1, f(-1)) a relative extreme minimum 
D)  (-5, f(-5)) is a relative extreme maximum point, (1, f(1)) a relative extreme minimum 
E)  (-5, f(-5)) is a relative extreme minimum point, (1, f(1)) a relative extreme maximum 
A)  (5, f(5)) is a relative extreme minimum point, (-1, f(-1)) a relative extreme maximum 
B)  (0, f(0)) is a relative extreme minimum point 
C)  (5, f(5)) is a relative extreme maximum point, (-1, f(-1)) a relative extreme minimum 
D)  (-5, f(-5)) is a relative extreme maximum point, (1, f(1)) a relative extreme minimum 
E)  (-5, f(-5)) is a relative extreme minimum point, (1, f(1)) a relative extreme maximum

Question 9

Determine the minimum value of x + y when xy = 100 (x > 0, y > 0).
Enter just an integer.

Accepted Answer

The answer of Determine the minimum value of x +...

Question 10

Is this the graph of a function having the following properties?
(I) concave down for all x
(II) asymptotic to the line x = 0

Accepted Answer

A) True 
 B)False

Question 11

Points A, B, and C lie on the graph of a function f(x), as shown on the diagram. What are the signs of f(x), f'(x), and f''(x) at the point C? Enter your answer as just "neg", "pos", or 0 in the order given above separated by commas.

Accepted Answer

The answer of Points A, B, and C lie on...

Question 12

A sports retailer expects to sell 120 sweat suits at a steady rate over the course of the coming year. The cost of placing an order with the wholesaler is $40. The annual inventory cost per sweat suit is $6 based on the average inventory level. Determine the economic order quantity for the suits (i.e., determine the order size that minimizes ordering and inventory expenses).
Enter just an integer (no words or units).

Accepted Answer

The answer of A sports retailer expects to sell 120...

Question 13

Which labeled point has the most positive slope?

Accepted Answer

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

Question 14

Which of the following is (are) true of $f ( x ) = 5 + 3 x ^ { 2 } - x ^ { 3 } ?$ 
(I) (1, 7) is a point of inflection 
(II) f(2) is a relative maximum point
(III) f has a relative minimum point at x = 0
(IV) f is increasing on (2, ?)

Accepted Answer

A)  II, III, and IV 
B)  I, II, and III 
C)  II and III 
D)  all of these 
E)  none of these 
A)  II, III, and IV 
B)  I, II, and III 
C)  II and III 
D)  all of these 
E)  none of these

Question 15

Find the interval(s) where f is increasing and concave down for $f ( x ) = \frac { 1 } { 4 } x ^ { 4 } - x ^ { 3 } + x ^ { 2 }$ Enter your answer in standard interval notation as either: (a, b) or (a, b)∪(c, d) where a< c with any irrational numbers in lowest terms of form: e ± $\frac { \sqrt { f } } { g }$

Accepted Answer

The answer of Find the interval(s) where f is increasing...

Question 16

Where is the function f(x) = $\frac { 5 } { ( 2 x - 4 ) ^ { 3 } }$ increasing?

Accepted Answer

A)  for x > 2 
B)  at x = 30 
C)  for all x 
D)  none of these 
A)  for x > 2 
B)  at x = 30 
C)  for all x 
D)  none of these

Question 17

Let a, b, and c be fixed numbers with a > 0 and let f(x) = $a x ^ { 2 }$ + bx + c. Which of the following properties is true of the graph of f(x) ?

Accepted Answer

A)  f(x) is always concave up 
B)  f(x) has either a relative maximum or inflection point 
C)  f(x) has one relative maximum 
D)  f(x) has one inflection point 
E)  none of these 
A)  f(x) is always concave up 
B)  f(x) has either a relative maximum or inflection point 
C)  f(x) has one relative maximum 
D)  f(x) has one inflection point 
E)  none of these

Question 18

A fast food restaurant is establishing its inventory policy for ordering frozen french fries. In the coming year, they expect to sell 2500 lbs of french fries. It costs $4 to place an order and the carrying costs for a year are $2 per pound based on the average amount in storage. The restaurant wishes to determine how many pounds of fries to order to minimize its ordering and inventory costs. Determine the optimal number of orders that should be placed and the optimal size of those orders.
Enter your answer exactly as just: a, b (both integers) where a represents the orders and b represents the lbs/order (no words or units).

Accepted Answer

The answer of A fast food restaurant is establishing its...

Question 19

Which of the following is the graph of f(x) = $x ^ { 4 }$ - 9?

Accepted Answer

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

Question 20

Is this the graph of y = $\sqrt { 3 x + 4 }$ ?

Accepted Answer

A) True 
 B)False

Determine the relative maximum point of $f ( x ) = x ^ { 3 } - 6 x ^ { 2 } + 9 x - 3$ Enter your answer as exactly just an ordered pair of integers: (a, b)

A manufacturer estimates that the profit from producing x units of a commodity is $- x ^ { 2 } + 40 x - 100$ dollars per week. What is the maximum profit he can realize in one week?

Find the relative minimum point(s) of $f ( x ) = \frac { x ^ { 4 } } { 4 } - x ^ { 3 } - 5 x ^ { 2 } - 10$

Find the inflection point(s) of $f ( x ) = \frac { 2 } { 3 } x ^ { 3 } - 7 x ^ { 2 } + 24 x - 16$ .

Find the x coordinates of all relative extreme points of $f ( x ) = \frac { 2 } { 3 } x ^ { 3 } - 7 x ^ { 2 } + 24 x - 72$

Is this the graph of a function having the following properties? (I) f'(x) < 0 for all x (II) f''(x) > 0 for all x < 0 (III) (0, 1) is a point on the graph

Find the relative extreme points for $f ( x ) = x ^ { 3 } + 6 x ^ { 2 } - 15 x$

Determine the minimum value of x + y when xy = 100 (x > 0, y > 0). Enter just an integer.

Is this the graph of a function having the following properties? (I) concave down for all x (II) asymptotic to the line x = 0

Points A, B, and C lie on the graph of a function f(x), as shown on the diagram. What are the signs of f(x), f'(x), and f''(x) at the point C? Enter your answer as just "neg", "pos", or 0 in the order given above separated by commas.

Which labeled point has the most positive slope?

Which of the following is (are) true of $f ( x ) = 5 + 3 x ^ { 2 } - x ^ { 3 } ?$ (I) (1, 7) is a point of inflection (II) f(2) is a relative maximum point (III) f has a relative minimum point at x = 0 (IV) f is increasing on (2, ?)

Where is the function f(x) = $\frac { 5 } { ( 2 x - 4 ) ^ { 3 } }$ increasing?

Let a, b, and c be fixed numbers with a > 0 and let f(x) = $a x ^ { 2 }$ + bx + c. Which of the following properties is true of the graph of f(x) ?

Which of the following is the graph of f(x) = $x ^ { 4 }$ - 9?

Is this the graph of y = $\sqrt { 3 x + 4 }$ ? $Is this the graph of y = \sqrt { 3 x + 4 } ?$

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 relative maximum point of f(x)=x3−6x2+9x−3f ( x ) = x ^ { 3 } - 6 x ^ { 2 } + 9 x - 3f(x)=x3−6x2+9x−3 Enter your answer as exactly just an ordered pair of integers: (a, b)

A manufacturer estimates that the profit from producing x units of a commodity is −x2+40x−100- x ^ { 2 } + 40 x - 100−x2+40x−100 dollars per week. What is the maximum profit he can realize in one week?

Find the relative minimum point(s) of f(x)=x44−x3−5x2−10f ( x ) = \frac { x ^ { 4 } } { 4 } - x ^ { 3 } - 5 x ^ { 2 } - 10f(x)=4x4​−x3−5x2−10

Find the inflection point(s) of f(x)=23x3−7x2+24x−16f ( x ) = \frac { 2 } { 3 } x ^ { 3 } - 7 x ^ { 2 } + 24 x - 16f(x)=32​x3−7x2+24x−16 .

This is the graph of f(x) = 13\frac { 1 } { 3 }31​ x3x ^ { 3 }x3 - 12\frac { 1 } { 2 }21​ x2x ^ { 2 }x2 - 6x. What is the inflection point? Enter your answer exactly as just an ordered pair of reduced fractions of form ab\frac { a } { b }ba​ , or integers (a, b), or the word "none".

Find the x coordinates of all relative extreme points of f(x)=23x3−7x2+24x−72f ( x ) = \frac { 2 } { 3 } x ^ { 3 } - 7 x ^ { 2 } + 24 x - 72f(x)=32​x3−7x2+24x−72

Is this the graph of a function having the following properties? (I) f'(x) < 0 for all x (II) f''(x) > 0 for all x < 0 (III) (0, 1) is a point on the graph

Find the relative extreme points for f(x)=x3+6x2−15xf ( x ) = x ^ { 3 } + 6 x ^ { 2 } - 15 xf(x)=x3+6x2−15x

Determine the minimum value of x + y when xy = 100 (x > 0, y > 0). Enter just an integer.

Is this the graph of a function having the following properties? (I) concave down for all x (II) asymptotic to the line x = 0

Points A, B, and C lie on the graph of a function f(x), as shown on the diagram. What are the signs of f(x), f'(x), and f''(x) at the point C? Enter your answer as just "neg", "pos", or 0 in the order given above separated by commas.

Which labeled point has the most positive slope?

Which of the following is (are) true of f(x)=5+3x2−x3?f ( x ) = 5 + 3 x ^ { 2 } - x ^ { 3 } ?f(x)=5+3x2−x3? (I) (1, 7) is a point of inflection (II) f(2) is a relative maximum point (III) f has a relative minimum point at x = 0 (IV) f is increasing on (2, ?)

Where is the function f(x) = 5(2x−4)3\frac { 5 } { ( 2 x - 4 ) ^ { 3 } }(2x−4)35​ increasing?

Let a, b, and c be fixed numbers with a > 0 and let f(x) = ax2a x ^ { 2 }ax2 + bx + c. Which of the following properties is true of the graph of f(x) ?

Which of the following is the graph of f(x) = x4x ^ { 4 }x4 - 9?

Is this the graph of y = 3x+4\sqrt { 3 x + 4 }3x+4​ ?

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 relative maximum point of $f ( x ) = x ^ { 3 } - 6 x ^ { 2 } + 9 x - 3$ Enter your answer as exactly just an ordered pair of integers: (a, b)

A manufacturer estimates that the profit from producing x units of a commodity is $- x ^ { 2 } + 40 x - 100$ dollars per week. What is the maximum profit he can realize in one week?

Find the relative minimum point(s) of $f ( x ) = \frac { x ^ { 4 } } { 4 } - x ^ { 3 } - 5 x ^ { 2 } - 10$

Find the inflection point(s) of $f ( x ) = \frac { 2 } { 3 } x ^ { 3 } - 7 x ^ { 2 } + 24 x - 16$ .

Find the x coordinates of all relative extreme points of $f ( x ) = \frac { 2 } { 3 } x ^ { 3 } - 7 x ^ { 2 } + 24 x - 72$

Find the relative extreme points for $f ( x ) = x ^ { 3 } + 6 x ^ { 2 } - 15 x$

Which of the following is (are) true of $f ( x ) = 5 + 3 x ^ { 2 } - x ^ { 3 } ?$ (I) (1, 7) is a point of inflection (II) f(2) is a relative maximum point (III) f has a relative minimum point at x = 0 (IV) f is increasing on (2, ?)

Where is the function f(x) = $\frac { 5 } { ( 2 x - 4 ) ^ { 3 } }$ increasing?

Let a, b, and c be fixed numbers with a > 0 and let f(x) = $a x ^ { 2 }$ + bx + c. Which of the following properties is true of the graph of f(x) ?

Which of the following is the graph of f(x) = $x ^ { 4 }$ - 9?

Is this the graph of y = $\sqrt { 3 x + 4 }$ ? $Is this the graph of y = \sqrt { 3 x + 4 } ?$