Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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## Problem Statement For \( f(x) \) shown below, which of the following graphs is \( f''(x) \)? ### Graph Descriptions 1. **Graph of \( f(x) \) (Top Middle):** - A green curve with a peak near \( x = 1 \) and a trough around \( x = -1.5 \). - It crosses the y-axis slightly above the origin. 2. **Option A (Bottom Left):** - A blue decreasing linear line. - Extends from around \( y = 7 \) at \( x = -3 \) to \( y = -10 \) at \( x = 3 \). 3. **Option B (Top Right):** - A purple parabola opening upwards. - Vertex at \( x = 0, y = -1 \). - Extends to around \( y = 3 \) for \( x = 2 \). 4. **Option C (Bottom Right):** - A yellow parabola opening downwards. - Vertex at \( x = 0, y = 3 \). - Extends to around \( y = -3 \) for \( x = -2 \). 5. **Option D (Bottom Middle):** - A straight line with a positive slope. - Extends from \( y = -6 \) at \( x = -3 \) to \( y = 10 \) at \( x = 3 \). ### Question Context The task is to select the correct graph of the second derivative \( f''(x) \) from the options provided, based on the behavior of the original function \( f(x) \). The second derivative represents the curvature of \( f(x) \), indicating concavity changes.
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Transcribed Image Text:## Problem Statement For \( f(x) \) shown below, which of the following graphs is \( f''(x) \)? ### Graph Descriptions 1. **Graph of \( f(x) \) (Top Middle):** - A green curve with a peak near \( x = 1 \) and a trough around \( x = -1.5 \). - It crosses the y-axis slightly above the origin. 2. **Option A (Bottom Left):** - A blue decreasing linear line. - Extends from around \( y = 7 \) at \( x = -3 \) to \( y = -10 \) at \( x = 3 \). 3. **Option B (Top Right):** - A purple parabola opening upwards. - Vertex at \( x = 0, y = -1 \). - Extends to around \( y = 3 \) for \( x = 2 \). 4. **Option C (Bottom Right):** - A yellow parabola opening downwards. - Vertex at \( x = 0, y = 3 \). - Extends to around \( y = -3 \) for \( x = -2 \). 5. **Option D (Bottom Middle):** - A straight line with a positive slope. - Extends from \( y = -6 \) at \( x = -3 \) to \( y = 10 \) at \( x = 3 \). ### Question Context The task is to select the correct graph of the second derivative \( f''(x) \) from the options provided, based on the behavior of the original function \( f(x) \). The second derivative represents the curvature of \( f(x) \), indicating concavity changes.
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