Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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**Transcription for Educational Website:** Title: Analyzing the Graph of a Derivative Text: Select the correct graph of the derivative of the function \( f(x) \) given below. **Graph Description:** The graph presented is a straight line with a negative slope, passing through the y-axis at approximately \( y = 4 \) and descending through the x-axis at approximately \( x = 2 \). This line continues to extend into the third quadrant, indicating a consistent decrease in value as \( x \) increases. This suggests that the derivative of the function is a linear function with a constant negative slope. **Analysis:** The linear nature of the graph implies that the original function \( f(x) \) is likely quadratic, as its derivative produces a linear expression. The negative slope of the derivative indicates that \( f(x) \) is decreasing consistently within this interval. The graph of the derivative is a crucial tool in understanding the behavior and changes in the original function.
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Transcribed Image Text:**Transcription for Educational Website:** Title: Analyzing the Graph of a Derivative Text: Select the correct graph of the derivative of the function \( f(x) \) given below. **Graph Description:** The graph presented is a straight line with a negative slope, passing through the y-axis at approximately \( y = 4 \) and descending through the x-axis at approximately \( x = 2 \). This line continues to extend into the third quadrant, indicating a consistent decrease in value as \( x \) increases. This suggests that the derivative of the function is a linear function with a constant negative slope. **Analysis:** The linear nature of the graph implies that the original function \( f(x) \) is likely quadratic, as its derivative produces a linear expression. The negative slope of the derivative indicates that \( f(x) \) is decreasing consistently within this interval. The graph of the derivative is a crucial tool in understanding the behavior and changes in the original function.
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