Question 1

Is this the graph of f(x) = $x ^ { 3 }$ - 3 $x ^ { 2 }$ + 2?

Accepted Answer

A) True 
 B)False

Question 2

A health food store stocks bottles of multivitamins. It orders equal quantities of stock from its wholesaler at equally spaced points throughout the year. The cost of replacing each order is $250. Moreover, the cost of keeping a jar of vitamins in inventory is $1 per year. The store predicts that it will sell 12,500 bottles of vitamins in the next year. How many orders of how many bottles each will result in a minimum cost to the health food store?
Enter your answer exactly as: a, b (integers) where a represents the number of orders and b represents the number of bottles in each order (no units or words).

Accepted Answer

The answer of A health food store stocks bottles of...

Question 3

Find the inflection point(s) of y = 2 $x ^ { 3 }$ - 3 $x ^ { 2 }$ - 12x + 17.

Accepted Answer

A)  $\left( \frac { 1 } { 2 } , \frac { 21 } { 2 } \right)$ 
B)  $\left( \frac { 1 } { 2 } , \frac { 21 } { 2 } \right)$ and $- \frac { 1 } { 2 } , 22$ 
C)  $\left( \frac { 7 } { 2 } , 24 \right.$ and $\left( \frac { 1 } { 2 } , \frac { 21 } { 2 } \right)$ 
D)  (2, -3) 
E)  none of these 
A)  $\left( \frac { 1 } { 2 } , \frac { 21 } { 2 } \right)$ 
B)  $\left( \frac { 1 } { 2 } , \frac { 21 } { 2 } \right)$ and $- \frac { 1 } { 2 } , 22$ 
C)  $\left( \frac { 7 } { 2 } , 24 \right.$ and $\left( \frac { 1 } { 2 } , \frac { 21 } { 2 } \right)$ 
D)  (2, -3) 
E)  none of these

Question 4

A toll road averages 36,000 cars per day when charging $1 (100 cents) per car. A survey concludes that changing the toll will result in 300 fewer cars for each cent of increase in price. Which of the following represents the revenue that will result from an increase of x cents in the price of the toll?

Accepted Answer

A)  (36,000 - 300x)(100 + x) 
B)  36,000(100 + x) - 300 x 
C)  36,000 + 300x + (100 + x) 
D)  36,000 ∙ 100 - x(300 - x) 
E)  none of these 
A)  (36,000 - 300x)(100 + x) 
B)  36,000(100 + x) - 300 x 
C)  36,000 + 300x + (100 + x) 
D)  36,000 ∙ 100 - x(300 - x) 
E)  none of these

Question 5

An open box with square ends is to be constructed with a volume of 125 cubic inches. The bottom is to be made of a material that weighs twice as much per square inch as the material used for the sides. What should the dimensions of the box be in order to minimize its weight? (Note: the actual weights of the materials do not matter.)Enter your answer exactly as a, b, c where these integers represent length, width, and height (no units or × symbols)

Accepted Answer

The answer of An open box with square ends is...

Question 6

Suppose f(x) is the function graphed below. Which of the following is f(x)?

Accepted Answer

A)  f(x) = $x ^ { 3 }$ + 5 
B)  f(x) = $\frac { 1 } { x }$ + $x ^ { 2 }$ + 3x 
C)  f(x) = $x ^ { 2 }$ + 3x 
D)  f(x) = $x ^ { 3 }$ + 6 $x ^ { 2 }$ + 9x 
E)  f(x) = - $x ^ { 2 }$ + 2x + 5 
A)  f(x) = $x ^ { 3 }$ + 5 
B)  f(x) = $\frac { 1 } { x }$ + $x ^ { 2 }$ + 3x 
C)  f(x) = $x ^ { 2 }$ + 3x 
D)  f(x) = $x ^ { 3 }$ + 6 $x ^ { 2 }$ + 9x 
E)  f(x) = - $x ^ { 2 }$ + 2x + 5

Question 7

Find the interval(s) where f is concave up for $f ( x ) = 4 x ^ { 4 } - 3 x ^ { 3 } + 5 x - 10$

Accepted Answer

A)  (-?, ?) 
B)  (-?, 0) ? $\left( \frac { 3 } { 8 } , \infty \right)$ 
C)  $\left( \frac { 3 } { 8 } , \infty \right)$ 
D)  $\left( - \infty , \frac { 3 } { 8 } \right)$ 
E)  $(\left. 0 , \frac { 3 } { 8 } \right)$ 
A)  (-?, ?) 
B)  (-?, 0) ? $\left( \frac { 3 } { 8 } , \infty \right)$ 
C)  $\left( \frac { 3 } { 8 } , \infty \right)$ 
D)  $\left( - \infty , \frac { 3 } { 8 } \right)$ 
E)  $(\left. 0 , \frac { 3 } { 8 } \right)$

Question 8

A rectangular corral with a total area of 60 square meters is to be fenced off and then divided into 2 rectangular sections by a fence down the middle.   The fencing for the outside costs $9 per running meter, whereas that for the interior dividing fence costs $12 per running meter. Which of the following statements hold, if the cost (c) of the fencing is to be maximized? (I) The constraint equation is 3w + 2 l = 60 .
(II) The objective equation is 2l ∙ w = 60 .
(III) The constraint equation is w ∙ l = 60 .
(IV) The objective equation is C = 30w + 18l .
(V) The constraint equation is C = 12w + 9wl .
(VI) The objective equation is C = 60 - lw .

Accepted Answer

A)  III and IV 
B)  V and VI 
C)  I and II 
D)  none of these 
A)  III and IV 
B)  V and VI 
C)  I and II 
D)  none of these

Question 9

Determine all the values of x where relative maximum and minimum points of the function $f ( x ) = \frac { 1 } { 3 } x ^ { 3 } - \frac { 3 } { 2 } x ^ { 2 } - 10 x$ occur. Distinguish the maxima from the minima using the second derivative rule. Enter your answer exactly as: f(a) rel max, f(b) rel min in that order.

Accepted Answer

f(-2) rel

Question 10

Which of the following is the graph of F(x) = 2x - $\frac { 1 } { x + 2 }$ + 5?

Accepted Answer

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

Question 11

Which of the following is (are) true of $f ( x ) = 3 x ^ { 2 / 3 } - 2 x ?$ 
(I) f is decreasing on (1, ?)
(II) (1, f(1)) is a relative minimum point 
(III) f is concave down everywhere
(IV) (0, 0) is an inflection point

Accepted Answer

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

Question 12

Is this the graph of g(x) = 2 $x ^ { 3 }$ + 3 $x ^ { 2 }$ - 12x - 5?

Accepted Answer

A) True 
 B)False

Question 13

Determine all maximum and minimum values of f(x) = - $x ^ { 3 }$ + 3 $x ^ { 2 }$ + 9x - 1 on $- 2 \leq x \leq 2 .$ Enter your answer exactly as: a,b both integers where a is the minimum of f and b is the maximum of f.

Accepted Answer

The answer of Determine all maximum and minimum values of...

Is this the graph of f(x) = $x ^ { 3 }$ - 3 $x ^ { 2 }$ + 2? $Is this the graph of f(x) = x ^ { 3 } - 3 x ^ { 2 } + 2?$

Find the inflection point(s) of y = 2 $x ^ { 3 }$ - 3 $x ^ { 2 }$ - 12x + 17.

Suppose f(x) is the function graphed below. Which of the following is f(x)?

Find the interval(s) where f is concave up for $f ( x ) = 4 x ^ { 4 } - 3 x ^ { 3 } + 5 x - 10$

Which of the following is the graph of F(x) = 2x - $\frac { 1 } { x + 2 }$ + 5?

Which of the following is (are) true of $f ( x ) = 3 x ^ { 2 / 3 } - 2 x ?$ (I) f is decreasing on (1, ?) (II) (1, f(1)) is a relative minimum point (III) f is concave down everywhere (IV) (0, 0) is an inflection point

Is this the graph of g(x) = 2 $x ^ { 3 }$ + 3 $x ^ { 2 }$ - 12x - 5? $Is this the graph of g(x) = 2 x ^ { 3 } + 3 x ^ { 2 } - 12x - 5?$

Determine all maximum and minimum values of f(x) = - $x ^ { 3 }$ + 3 $x ^ { 2 }$ + 9x - 1 on $- 2 \leq x \leq 2 .$ Enter your answer exactly as: a,b both integers where a is the minimum of f and b is the maximum of f.

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

Is this the graph of f(x) = x3x ^ { 3 }x3 - 3 x2x ^ { 2 }x2 + 2?

Find the inflection point(s) of y = 2 x3x ^ { 3 }x3 - 3 x2x ^ { 2 }x2 - 12x + 17.

Suppose f(x) is the function graphed below. Which of the following is f(x)?

Find the interval(s) where f is concave up for f(x)=4x4−3x3+5x−10f ( x ) = 4 x ^ { 4 } - 3 x ^ { 3 } + 5 x - 10f(x)=4x4−3x3+5x−10

Which of the following is the graph of F(x) = 2x - 1x+2\frac { 1 } { x + 2 }x+21​ + 5?

Which of the following is (are) true of f(x)=3x2/3−2x?f ( x ) = 3 x ^ { 2 / 3 } - 2 x ?f(x)=3x2/3−2x? (I) f is decreasing on (1, ?) (II) (1, f(1)) is a relative minimum point (III) f is concave down everywhere (IV) (0, 0) is an inflection point

Is this the graph of g(x) = 2 x3x ^ { 3 }x3 + 3 x2x ^ { 2 }x2 - 12x - 5?

Determine all maximum and minimum values of f(x) = - x3x ^ { 3 }x3 + 3 x2x ^ { 2 }x2 + 9x - 1 on −2≤x≤2.- 2 \leq x \leq 2 .−2≤x≤2. Enter your answer exactly as: a,b both integers where a is the minimum of f and b is the maximum of f.

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

Is this the graph of f(x) = $x ^ { 3 }$ - 3 $x ^ { 2 }$ + 2? $Is this the graph of f(x) = x ^ { 3 } - 3 x ^ { 2 } + 2?$

Find the inflection point(s) of y = 2 $x ^ { 3 }$ - 3 $x ^ { 2 }$ - 12x + 17.

Find the interval(s) where f is concave up for $f ( x ) = 4 x ^ { 4 } - 3 x ^ { 3 } + 5 x - 10$

Which of the following is the graph of F(x) = 2x - $\frac { 1 } { x + 2 }$ + 5?

Which of the following is (are) true of $f ( x ) = 3 x ^ { 2 / 3 } - 2 x ?$ (I) f is decreasing on (1, ?) (II) (1, f(1)) is a relative minimum point (III) f is concave down everywhere (IV) (0, 0) is an inflection point

Is this the graph of g(x) = 2 $x ^ { 3 }$ + 3 $x ^ { 2 }$ - 12x - 5? $Is this the graph of g(x) = 2 x ^ { 3 } + 3 x ^ { 2 } - 12x - 5?$

Determine all maximum and minimum values of f(x) = - $x ^ { 3 }$ + 3 $x ^ { 2 }$ + 9x - 1 on $- 2 \leq x \leq 2 .$ Enter your answer exactly as: a,b both integers where a is the minimum of f and b is the maximum of f.