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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+ 14 ·1 -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+ 14 ·1 -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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### Educational Resource: Understanding Antiderivatives **Question:** Which of the following graphs (a)–(d) could represent an antiderivative of the function shown in Figure 6.3? **Graph Details:** - **Figure 6.3** shows a graph on a coordinate plane with the vertical axis labeled \(y\) and the horizontal axis labeled \(x\). - The graph is a curve that starts below the \(x\)-axis, moves upwards, and crosses the \(x\)-axis around \(x = -1\). - As \(x\) increases past zero, the curve continues to rise steeply. **Axes Values:** - The \(y\)-values range from \(-27\) to \(27\) marked in increments of 9. - The \(x\)-values range from \(-3\) to \(3\) marked in increments of 1. **Graph Behavior:** - The function shows an increasing trend, with the steepness increasing as \(x\) becomes more positive. - The curve suggests a continuous function with no breaks or discontinuities. **Conceptual Focus:** - Consider which characteristics of the graph reflect properties of a potential antiderivative. An antiderivative (or indefinite integral) of a function is a function whose derivative is the original function. - Analyze how the slope of the original function, which represents the derivative of its antiderivative, might translate into the shape and behavior of its antiderivative graph. By understanding these aspects, students can determine which graph might represent a valid antiderivative for the function displayed in Figure 6.3.
Transcribed Image Text:### Educational Resource: Understanding Antiderivatives **Question:** Which of the following graphs (a)–(d) could represent an antiderivative of the function shown in Figure 6.3? **Graph Details:** - **Figure 6.3** shows a graph on a coordinate plane with the vertical axis labeled \(y\) and the horizontal axis labeled \(x\). - The graph is a curve that starts below the \(x\)-axis, moves upwards, and crosses the \(x\)-axis around \(x = -1\). - As \(x\) increases past zero, the curve continues to rise steeply. **Axes Values:** - The \(y\)-values range from \(-27\) to \(27\) marked in increments of 9. - The \(x\)-values range from \(-3\) to \(3\) marked in increments of 1. **Graph Behavior:** - The function shows an increasing trend, with the steepness increasing as \(x\) becomes more positive. - The curve suggests a continuous function with no breaks or discontinuities. **Conceptual Focus:** - Consider which characteristics of the graph reflect properties of a potential antiderivative. An antiderivative (or indefinite integral) of a function is a function whose derivative is the original function. - Analyze how the slope of the original function, which represents the derivative of its antiderivative, might translate into the shape and behavior of its antiderivative graph. By understanding these aspects, students can determine which graph might represent a valid antiderivative for the function displayed in Figure 6.3.
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