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The slope graph of f has a [Select] x = 0

The slope graph of f has a [Select] x = 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The text from the image is as follows: "The slope graph of \( f \) has a [Select] at \( x = 0 \)." There are no graphs or diagrams provided in the image.
Transcribed Image Text:The text from the image is as follows: "The slope graph of \( f \) has a [Select] at \( x = 0 \)." There are no graphs or diagrams provided in the image.
Consider this graph of the function \( f \) to answer the questions below: ### Explanation of the Graph: The graph depicts a function \( f(x) \) over the range \( x = -9 \) to \( x = 9 \). - **Endpoints**: - As \( x \to -9 \), the function continues to rise. - At \( x = -6 \), there is an open circle on the graph indicating that the function \( f(x) \) is not defined at \( x = -6 \). - **Key Points**: - The function increases sharply from the left, reaching a maximum at \( x = -3 \) where \( f(x) = 5 \). - Post maximum, the function decreases, crossing the x-axis at \( x = 0 \). - The function then reaches a local minimum at \( x = 3 \) where \( f(x) = -2 \). - After the minimum, the function increases again, crossing the x-axis at approximately \( x = 5 \). - **Arrow Indicators**: - On the left, the graph is denoted with an arrow pointing left, suggesting that the function continues indefinitely in the negative x-direction. - On the right, an arrow points downward, indicating the function continues to decrease beyond \( x = 7 \). The graph visually represents the different behaviors and critical points of the function \( f(x) \).
Transcribed Image Text:Consider this graph of the function \( f \) to answer the questions below: ### Explanation of the Graph: The graph depicts a function \( f(x) \) over the range \( x = -9 \) to \( x = 9 \). - **Endpoints**: - As \( x \to -9 \), the function continues to rise. - At \( x = -6 \), there is an open circle on the graph indicating that the function \( f(x) \) is not defined at \( x = -6 \). - **Key Points**: - The function increases sharply from the left, reaching a maximum at \( x = -3 \) where \( f(x) = 5 \). - Post maximum, the function decreases, crossing the x-axis at \( x = 0 \). - The function then reaches a local minimum at \( x = 3 \) where \( f(x) = -2 \). - After the minimum, the function increases again, crossing the x-axis at approximately \( x = 5 \). - **Arrow Indicators**: - On the left, the graph is denoted with an arrow pointing left, suggesting that the function continues indefinitely in the negative x-direction. - On the right, an arrow points downward, indicating the function continues to decrease beyond \( x = 7 \). The graph visually represents the different behaviors and critical points of the function \( f(x) \).
Expert Solution
Step 1: Introduction

The slope is negative for a decreasing function and 

The slope is positive for an increasing function .


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