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Select the correct graph of the derivative of the function f(x) given below. -4 -2 -2 -4 12 4 X

Select the correct graph of the derivative of the function f(x) given below. -4 -2 -2 -4 12 4 X

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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Question
**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.
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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