Exam 2: Applications of the Derivative

An airline flies 120,000 passengers per week to Florida when charging $100 per flight. It estimates that for each $1 increase in price it will lose 400 passengers. By how much should the fare be increased (or decreased) to maximize total revenue? Enter your answer as just an integer (no symbols or words).

(Short Answer)

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Question 41

Is this the graph of a function having the following properties? (I) asymptotic to the line y = $\frac { 1 } { 2 }$ x - 1 (II) relative maximum at x = 0 $Is this the graph of a function having the following properties? (I) asymptotic to the line y = \frac { 1 } { 2 } x - 1 (II) relative maximum at x = 0$

(True/False)

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Question 42

Which of the following could represent a function having the given properties? (I) increasing slope for x < 4 (II) f'(x) > 0 for all x (x ≠ 4) (III) asymptote at x = 4

(Multiple Choice)

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Question 43

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, f''(x) < 0 for x >0 (III) asymptotes at y = $\frac { \pi } { 2 }$ , y = - $\frac { \pi } { 2 }$ $Is this the graph of a function having the following properties? (I) f'(x) > 0 for all x (II) f''(x) > 0 for all x < 0, f''(x) < 0 for x >0 (III) asymptotes at y = \frac { \pi } { 2 } , y = - \frac { \pi } { 2 }$

(True/False)

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Question 44

Is this the graph of f(x) = $( x - 2 ) ^ { 3 }$ + 1? $Is this the graph of f(x) = ( x - 2 ) ^ { 3 } + 1?$

(True/False)

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Question 45

Is this the graph of h(x) = x + 10 + $\frac { 9 } { x }$ ? Enter just the word "yes" or "no" (lower case). $Is this the graph of h(x) = x + 10 + \frac { 9 } { x } ? Enter just the word yes or no (lower case).$

(True/False)

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Question 46

Is this the graph of the function f(x) = $- x ^ { 3 }$ + 3 $x ^ { 2 }$ + 9x - 15? $Is this the graph of the function f(x) = - x ^ { 3 } + 3 x ^ { 2 } + 9x - 15?$

(True/False)

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Question 47

Is this the graph of f(x) = 9x + 1 + $\frac { 1 } { x }$ , x > 0? $Is this the graph of f(x) = 9x + 1 + \frac { 1 } { x } , x > 0?$

(True/False)

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Question 48

Determine the minimum value of f(x) = $x ^ { 3 }$ - 3 $x ^ { 2 }$ + 2 on 1 ≤ x ≤ 3. Enter just an integer.

(Short Answer)

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Question 49

Find the maximum value of the function f(x) = - $x ^ { 3 }$ + 6 $x ^ { 2 }$ + 10 for x ≥ 0. Enter your answer exactly as: f(a) = b rel max

(Short Answer)

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Question 50

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

(Multiple Choice)

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Question 51

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

(Multiple Choice)

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Question 52

Determine the minimum value of $f ( x ) = x + \frac { 1 } { x - 1 } \text { on } x > 1$ Enter just an integer.

(Short Answer)

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Question 53

Let F(x) be the function graphed below. For what value is F'(x) > 0?

(Multiple Choice)

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Question 54

Find the x coordinates of all relative extreme points of $f ( x ) = \frac { 1 } { 2 } x ^ { 4 } - \frac { 2 } { 3 } x ^ { 3 } - 6 x ^ { 2 } - 100$

(Multiple Choice)

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Question 55

A rectangular garden is to be fenced in and divided into three parallel sections. The fencing for the boundary costs $20 per foot whereas the fencing for the dividing fences costs $5 per foot. Consider the problem of finding the dimensions of the largest garden possible if the gardener can spend $2000 for the fencing. Find the values of l and w for which the total area of the garden is as large as possible.

(Short Answer)

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Question 56

Which of the following best represents the graph of y = 2 $x ^ { 3 }$ - 3 $x ^ { 2 }$ - 12x + 17 near the point (2, -3)?

(Multiple Choice)

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Question 57

Determine the maximum and minimum values of f(x) = $x ^ { 3 }$ - 3 $x ^ { 2 }$ - 9x on -4 ≤ x ≤ 4 . Enter your answer exactly as: a,b both integers where a is the minimum of f and b is the maximum of f.

(Short Answer)

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Question 58

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

(Multiple Choice)

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Question 59

A health club offers memberships at the rate of $300, provided that at least 50 people join. For each member in excess of 50, the membership fee will be reduced by $2 for all members. Due to space limitations, at most 125 memberships will be sold. How many memberships should the club sell in order to maximize its revenue?

(Multiple Choice)

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Question 60

Showing 41 - 60 of 93

Which of the following could represent a function having the given properties? (I) increasing slope for x < 4 (II) f'(x) > 0 for all x (x ≠ 4) (III) asymptote at x = 4

Is this the graph of f(x) = $( x - 2 ) ^ { 3 }$ + 1? $Is this the graph of f(x) = ( x - 2 ) ^ { 3 } + 1?$

Is this the graph of h(x) = x + 10 + $\frac { 9 } { x }$ ? Enter just the word "yes" or "no" (lower case). $Is this the graph of h(x) = x + 10 + \frac { 9 } { x } ? Enter just the word yes or no (lower case).$

Is this the graph of the function f(x) = $- x ^ { 3 }$ + 3 $x ^ { 2 }$ + 9x - 15? $Is this the graph of the function f(x) = - x ^ { 3 } + 3 x ^ { 2 } + 9x - 15?$

Is this the graph of f(x) = 9x + 1 + $\frac { 1 } { x }$ , x > 0? $Is this the graph of f(x) = 9x + 1 + \frac { 1 } { x } , x > 0?$

Determine the minimum value of f(x) = $x ^ { 3 }$ - 3 $x ^ { 2 }$ + 2 on 1 ≤ x ≤ 3. Enter just an integer.

Find the maximum value of the function f(x) = - $x ^ { 3 }$ + 6 $x ^ { 2 }$ + 10 for x ≥ 0. Enter your answer exactly as: f(a) = b rel max

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

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

Determine the minimum value of $f ( x ) = x + \frac { 1 } { x - 1 } \text { on } x > 1$ Enter just an integer.

Let F(x) be the function graphed below. For what value is F'(x) > 0?

Find the x coordinates of all relative extreme points of $f ( x ) = \frac { 1 } { 2 } x ^ { 4 } - \frac { 2 } { 3 } x ^ { 3 } - 6 x ^ { 2 } - 100$

Which of the following best represents the graph of y = 2 $x ^ { 3 }$ - 3 $x ^ { 2 }$ - 12x + 17 near the point (2, -3)?

Determine the maximum and minimum values of f(x) = $x ^ { 3 }$ - 3 $x ^ { 2 }$ - 9x on -4 ≤ x ≤ 4 . Enter your answer exactly as: a,b both integers where a is the minimum of f and b is the maximum of f.

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

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 a function having the following properties? (I) asymptotic to the line y = 12\frac { 1 } { 2 }21​ x - 1 (II) relative maximum at x = 0

Which of the following could represent a function having the given properties? (I) increasing slope for x < 4 (II) f'(x) > 0 for all x (x ≠ 4) (III) asymptote at x = 4

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, f''(x) < 0 for x >0 (III) asymptotes at y = π2\frac { \pi } { 2 }2π​ , y = - π2\frac { \pi } { 2 }2π​

Is this the graph of f(x) = (x−2)3( x - 2 ) ^ { 3 }(x−2)3 + 1?

Is this the graph of h(x) = x + 10 + 9x\frac { 9 } { x }x9​ ? Enter just the word "yes" or "no" (lower case).

Is this the graph of the function f(x) = −x3- x ^ { 3 }−x3 + 3 x2x ^ { 2 }x2 + 9x - 15?

Is this the graph of f(x) = 9x + 1 + 1x\frac { 1 } { x }x1​ , x > 0?

Determine the minimum value of f(x) = x3x ^ { 3 }x3 - 3 x2x ^ { 2 }x2 + 2 on 1 ≤ x ≤ 3. Enter just an integer.

Find the maximum value of the function f(x) = - x3x ^ { 3 }x3 + 6 x2x ^ { 2 }x2 + 10 for x ≥ 0. Enter your answer exactly as: f(a) = b rel max

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

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

Determine the minimum value of f(x)=x+1x−1 on x>1f ( x ) = x + \frac { 1 } { x - 1 } \text { on } x > 1f(x)=x+x−11​ on x>1 Enter just an integer.

Let F(x) be the function graphed below. For what value is F'(x) > 0?

Find the x coordinates of all relative extreme points of f(x)=12x4−23x3−6x2−100f ( x ) = \frac { 1 } { 2 } x ^ { 4 } - \frac { 2 } { 3 } x ^ { 3 } - 6 x ^ { 2 } - 100f(x)=21​x4−32​x3−6x2−100

Which of the following best represents the graph of y = 2 x3x ^ { 3 }x3 - 3 x2x ^ { 2 }x2 - 12x + 17 near the point (2, -3)?

Determine the maximum and minimum values of f(x) = x3x ^ { 3 }x3 - 3 x2x ^ { 2 }x2 - 9x on -4 ≤ x ≤ 4 . Enter your answer exactly as: a,b both integers where a is the minimum of f and b is the maximum of f.

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

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) = $( x - 2 ) ^ { 3 }$ + 1? $Is this the graph of f(x) = ( x - 2 ) ^ { 3 } + 1?$

Is this the graph of h(x) = x + 10 + $\frac { 9 } { x }$ ? Enter just the word "yes" or "no" (lower case). $Is this the graph of h(x) = x + 10 + \frac { 9 } { x } ? Enter just the word yes or no (lower case).$

Is this the graph of the function f(x) = $- x ^ { 3 }$ + 3 $x ^ { 2 }$ + 9x - 15? $Is this the graph of the function f(x) = - x ^ { 3 } + 3 x ^ { 2 } + 9x - 15?$

Is this the graph of f(x) = 9x + 1 + $\frac { 1 } { x }$ , x > 0? $Is this the graph of f(x) = 9x + 1 + \frac { 1 } { x } , x > 0?$

Determine the minimum value of f(x) = $x ^ { 3 }$ - 3 $x ^ { 2 }$ + 2 on 1 ≤ x ≤ 3. Enter just an integer.

Find the maximum value of the function f(x) = - $x ^ { 3 }$ + 6 $x ^ { 2 }$ + 10 for x ≥ 0. Enter your answer exactly as: f(a) = b rel max

Determine the minimum value of $f ( x ) = x + \frac { 1 } { x - 1 } \text { on } x > 1$ Enter just an integer.

Find the x coordinates of all relative extreme points of $f ( x ) = \frac { 1 } { 2 } x ^ { 4 } - \frac { 2 } { 3 } x ^ { 3 } - 6 x ^ { 2 } - 100$

Which of the following best represents the graph of y = 2 $x ^ { 3 }$ - 3 $x ^ { 2 }$ - 12x + 17 near the point (2, -3)?

Determine the maximum and minimum values of f(x) = $x ^ { 3 }$ - 3 $x ^ { 2 }$ - 9x on -4 ≤ x ≤ 4 . Enter your answer exactly as: a,b both integers where a is the minimum of f and b is the maximum of f.