The graph of a derivative f' (x) is shown in the figure below. 9 1 X 2 f (x) 3 Enter the exact answers. 0 4 Fill in the table of values for f(x) given that f(0) = 3. 3 5 i f'(x) 1 +x 6 i 2 i 3 i i i 6
The graph of a derivative f' (x) is shown in the figure below. 9 1 X 2 f (x) 3 Enter the exact answers. 0 4 Fill in the table of values for f(x) given that f(0) = 3. 3 5 i f'(x) 1 +x 6 i 2 i 3 i i i 6
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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Question
![The graph of a derivative \( f'(x) \) is shown in the figure below.
*Graph Description:*
- The graph has \( x \)-axis values ranging from 0 to 6.
- For \( 0 \leq x < 2 \), \( f'(x) = -9 \).
- At \( x = 2 \), \( f'(x) jumps to 0 and remains 0 until \( x = 4 \).
- At \( x = 4 \), \( f'(x) jumps to 9 and remains 9 until \( x = 6 \).
Fill in the table of values for \( f(x) \) given that \( f(0) = 3 \).
Enter the exact answers.
\[
\begin{array}{|c|c|c|c|c|c|c|c|}
\hline
x & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\
\hline
f(x) & 3 & \text{[ ]} & \text{[ ]} & \text{[ ]} & \text{[ ]} & \text{[ ]} & \text{[ ]} \\
\hline
\end{array}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff1ac4a5c-5c91-4743-9545-fc03c7695e62%2Fb9ac9eb7-2e67-45b2-b0df-6ec1869bc3b4%2F6nx7ebg_processed.png&w=3840&q=75)
Transcribed Image Text:The graph of a derivative \( f'(x) \) is shown in the figure below.
*Graph Description:*
- The graph has \( x \)-axis values ranging from 0 to 6.
- For \( 0 \leq x < 2 \), \( f'(x) = -9 \).
- At \( x = 2 \), \( f'(x) jumps to 0 and remains 0 until \( x = 4 \).
- At \( x = 4 \), \( f'(x) jumps to 9 and remains 9 until \( x = 6 \).
Fill in the table of values for \( f(x) \) given that \( f(0) = 3 \).
Enter the exact answers.
\[
\begin{array}{|c|c|c|c|c|c|c|c|}
\hline
x & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\
\hline
f(x) & 3 & \text{[ ]} & \text{[ ]} & \text{[ ]} & \text{[ ]} & \text{[ ]} & \text{[ ]} \\
\hline
\end{array}
\]
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