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Which of the following graphs (a)-(d) could represent an antiderivative of the function shown in Figure 6.3? Y 27 18+ 9+ I form -9+ -18+ -27+ Figure 6.3

Which of the following graphs (a)-(d) could represent an antiderivative of the function shown in Figure 6.3? Y 27 18+ 9+ I form -9+ -18+ -27+ Figure 6.3

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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find antiderivative of the function in the graph

**Transcription for Educational Website:** **Text:** "Which of the following graphs (a)–(d) could represent an antiderivative of the function shown in Figure 6.3?" **Explanation of Graph (Figure 6.3):** The graph in Figure 6.3 is a curve plotted on a Cartesian coordinate system with the x-axis and y-axis intersecting at the origin (0,0). The axes are labeled with "x" for the horizontal axis and "y" for the vertical axis. The graph displays the following details: - **Curve Description:** The curve shown is an increasing function with a steep slope as it moves from left to right. Starting from the lower-left part of the graph, the curve rises steadily, crossing just above -1 on the y-axis when x is approximately 0.5. It continues to increase more steeply as the value of x increases. - **Axes Markings:** - The x-axis is marked with values: -3, -2, -1, 0, 1, 2, 3 - The y-axis is marked with values: -27, -18, -9, 0, 9, 18, 27 - **Key Points:** - Where the curve crosses the y-axis it is slightly above -1, suggesting that the value approaches zero as x tends to zero. - As x approaches positive values, the curve sharply rises, indicating potential exponential or polynomial behavior. - **Overall Shape:** The shape of the graph indicates a function that starts negative and increases toward very positive values as x moves from negative to positive. This detailed explanation is intended to help students understand the critical characteristics of the graph that might relate to its antiderivatives.
Transcribed Image Text:**Transcription for Educational Website:** **Text:** "Which of the following graphs (a)–(d) could represent an antiderivative of the function shown in Figure 6.3?" **Explanation of Graph (Figure 6.3):** The graph in Figure 6.3 is a curve plotted on a Cartesian coordinate system with the x-axis and y-axis intersecting at the origin (0,0). The axes are labeled with "x" for the horizontal axis and "y" for the vertical axis. The graph displays the following details: - **Curve Description:** The curve shown is an increasing function with a steep slope as it moves from left to right. Starting from the lower-left part of the graph, the curve rises steadily, crossing just above -1 on the y-axis when x is approximately 0.5. It continues to increase more steeply as the value of x increases. - **Axes Markings:** - The x-axis is marked with values: -3, -2, -1, 0, 1, 2, 3 - The y-axis is marked with values: -27, -18, -9, 0, 9, 18, 27 - **Key Points:** - Where the curve crosses the y-axis it is slightly above -1, suggesting that the value approaches zero as x tends to zero. - As x approaches positive values, the curve sharply rises, indicating potential exponential or polynomial behavior. - **Overall Shape:** The shape of the graph indicates a function that starts negative and increases toward very positive values as x moves from negative to positive. This detailed explanation is intended to help students understand the critical characteristics of the graph that might relate to its antiderivatives.
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