Suppose F(t) has the derivative f(t) shown below, and F(0) = 6. Find values for F(1) and F(8) -1 3 2 1 -1 -2 -3 F(1) = F(8) = N 2 3 45 5 6 7 8
Suppose F(t) has the derivative f(t) shown below, and F(0) = 6. Find values for F(1) and F(8) -1 3 2 1 -1 -2 -3 F(1) = F(8) = N 2 3 45 5 6 7 8
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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![Suppose \( F(t) \) has the derivative \( f(t) \) shown below, and \( F(0) = 6 \). Find values for \( F(1) \) and \( F(8) \).
**Graph Description:**
- The graph shows a piecewise linear function of \( f(t) = F'(t) \) plotted against \( t \).
- The x-axis ranges from 0 to 8.
- The y-axis ranges from -3 to 3.
- Key points on the graph include:
- From \( t = 0 \) to \( t = 1 \), the graph descends linearly from \( (0, 0) \) to \( (1, -1) \).
- From \( t = 1 \) to \( t = 3 \), the graph ascends linearly from \( (1, -1) \) to \( (3, 1) \).
- From \( t = 3 \) to \( t = 6 \), the graph continues to ascend linearly from \( (3, 1) \) to \( (6, 3) \).
- From \( t = 6 \) to \( t = 8 \), the graph is a horizontal line at \( y = 3 \).
**Questions:**
1. \( F(1) = \) [Input Box]
2. \( F(8) = \) [Input Box]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F57a80892-6d38-4c33-b12d-e676cd98c4f8%2F9e85312d-2c23-4da1-8fa6-0ff9bb7b5a17%2F2srt2fs_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose \( F(t) \) has the derivative \( f(t) \) shown below, and \( F(0) = 6 \). Find values for \( F(1) \) and \( F(8) \).
**Graph Description:**
- The graph shows a piecewise linear function of \( f(t) = F'(t) \) plotted against \( t \).
- The x-axis ranges from 0 to 8.
- The y-axis ranges from -3 to 3.
- Key points on the graph include:
- From \( t = 0 \) to \( t = 1 \), the graph descends linearly from \( (0, 0) \) to \( (1, -1) \).
- From \( t = 1 \) to \( t = 3 \), the graph ascends linearly from \( (1, -1) \) to \( (3, 1) \).
- From \( t = 3 \) to \( t = 6 \), the graph continues to ascend linearly from \( (3, 1) \) to \( (6, 3) \).
- From \( t = 6 \) to \( t = 8 \), the graph is a horizontal line at \( y = 3 \).
**Questions:**
1. \( F(1) = \) [Input Box]
2. \( F(8) = \) [Input Box]
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