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graph of the derivative f. -2 2 -2 2 XI

graph of the derivative f. -2 2 -2 2 XI

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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The image contains three graphs labeled as options c, d, and e. **Graph c:** - This graph displays a sinusoidal wave, suggesting it represents a trigonometric function, likely either sine or cosine. - The x-axis ranges from -3 to 3, and the y-axis ranges from -2 to 2. - The wave oscillates above and below the x-axis, completing one full cycle within this range. **Graph d:** - This graph appears to represent a horizontal line, indicating a constant function. - The x-axis ranges from -6 to 6, and the y-axis remains at 0. - The line is exactly along the x-axis, signifying that the output value does not change regardless of the input. **Graph e:** - This graph illustrates a curve with a vertical asymptote and a horizontal asymptote, typical of a rational function. - The x-axis ranges from -2 to 2 and seems to curve dramatically as it approaches these bounds. - The y-axis ranges from -12 to 12. The curve appears to approach infinity as x approaches a certain point, characteristic of asymptotic behavior. These graphs serve as visual aids for understanding the behavior and properties of different mathematical functions.
Transcribed Image Text:The image contains three graphs labeled as options c, d, and e. **Graph c:** - This graph displays a sinusoidal wave, suggesting it represents a trigonometric function, likely either sine or cosine. - The x-axis ranges from -3 to 3, and the y-axis ranges from -2 to 2. - The wave oscillates above and below the x-axis, completing one full cycle within this range. **Graph d:** - This graph appears to represent a horizontal line, indicating a constant function. - The x-axis ranges from -6 to 6, and the y-axis remains at 0. - The line is exactly along the x-axis, signifying that the output value does not change regardless of the input. **Graph e:** - This graph illustrates a curve with a vertical asymptote and a horizontal asymptote, typical of a rational function. - The x-axis ranges from -2 to 2 and seems to curve dramatically as it approaches these bounds. - The y-axis ranges from -12 to 12. The curve appears to approach infinity as x approaches a certain point, characteristic of asymptotic behavior. These graphs serve as visual aids for understanding the behavior and properties of different mathematical functions.
The image displays a problem involving the graph of a function's derivative, \( f' \). ### Graph Description: 1. **First Graph**: - This graph is of the function \( f' \). - The graph plots a curve that starts from the bottom left, rises to a peak around \( x = 3 \), and then descends towards \( x = 5 \). - The inflection points appear around the relative maximum. 2. **Multiple Choice Options**: - **Option a**: - The graph shows a curve that starts at around \( y = 4 \) on the left side and asymptotically approaches zero on the right. - It has a steep curve heading downwards from left to right. - **Option b**: - This graph is a horizontal line at approximately \( y = 1 \). - The line is straight, indicating no change along the x-axis. ### Task: - **Select one**: - \( \circ \) a. - \( \circ \) b. This problem involves understanding the derivatives of functions and interpreting their graphical representations. By analyzing the graphs, one can determine the behavior of a function based on its derivative.
Transcribed Image Text:The image displays a problem involving the graph of a function's derivative, \( f' \). ### Graph Description: 1. **First Graph**: - This graph is of the function \( f' \). - The graph plots a curve that starts from the bottom left, rises to a peak around \( x = 3 \), and then descends towards \( x = 5 \). - The inflection points appear around the relative maximum. 2. **Multiple Choice Options**: - **Option a**: - The graph shows a curve that starts at around \( y = 4 \) on the left side and asymptotically approaches zero on the right. - It has a steep curve heading downwards from left to right. - **Option b**: - This graph is a horizontal line at approximately \( y = 1 \). - The line is straight, indicating no change along the x-axis. ### Task: - **Select one**: - \( \circ \) a. - \( \circ \) b. This problem involves understanding the derivatives of functions and interpreting their graphical representations. By analyzing the graphs, one can determine the behavior of a function based on its derivative.
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The graph of the function fx is 

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To Sketch: The graph of the derivative f'x

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