Using the graphing utility, graph the function y = f'(x). f'(x) = x* – 15x³ + 73x² – 129x + 70 %3D f' (x) = y -400 200 -40 -20 20 40 -200 -400 powered by desmos -600 +
Using the graphing utility, graph the function y = f'(x). f'(x) = x* – 15x³ + 73x² – 129x + 70 %3D f' (x) = y -400 200 -40 -20 20 40 -200 -400 powered by desmos -600 +
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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![### Using the Graphing Utility to Graph a Function
To graph the function \( y = f'(x) \), use the provided equation:
\[ f'(x) = x^4 - 15x^3 + 73x^2 - 129x + 70 \]
#### Graphing Area
Below the equation, there is an interactive graphing area where you can input the function to visualize its behavior.
- The x-axis ranges from \(-40\) to \(40\).
- The y-axis ranges from \(-600\) to \(400\).
The graph displays a grid with lines at intervals of 20 along the x-axis and 200 along the y-axis. You can zoom in and out using the plus and minus buttons, and reset the view if needed using the home button. This interactive feature allows for a detailed examination of the function's characteristics.
Use the input box labeled \( f'(x) = \) to enter the given function and observe the resulting graph to analyze the polynomial's features, such as roots, turning points, and behavior at infinity.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F07bee885-b193-43d8-ac2a-8488a7e88bc2%2F6fcc5a27-afad-481e-b01d-272cde8f2447%2Fs08ufxo_processed.png&w=3840&q=75)
Transcribed Image Text:### Using the Graphing Utility to Graph a Function
To graph the function \( y = f'(x) \), use the provided equation:
\[ f'(x) = x^4 - 15x^3 + 73x^2 - 129x + 70 \]
#### Graphing Area
Below the equation, there is an interactive graphing area where you can input the function to visualize its behavior.
- The x-axis ranges from \(-40\) to \(40\).
- The y-axis ranges from \(-600\) to \(400\).
The graph displays a grid with lines at intervals of 20 along the x-axis and 200 along the y-axis. You can zoom in and out using the plus and minus buttons, and reset the view if needed using the home button. This interactive feature allows for a detailed examination of the function's characteristics.
Use the input box labeled \( f'(x) = \) to enter the given function and observe the resulting graph to analyze the polynomial's features, such as roots, turning points, and behavior at infinity.
![**Instructions for Analyzing the Graph of a Function \( f \)**
1. **Finding Points of Inflection:**
- Use the graph to identify the point(s) of inflection of the function \( f \).
- Provide your answer as a comma-separated list of values in the form of exact numbers. Utilize symbolic notation and fractions where necessary.
- If the function has no inflection points, enter "DNE" (Does Not Exist).
**Input Box for Points of Inflection:**
\[
x = \underline{\hspace{3cm}}
\]
2. **Determining Intervals of Concavity:**
- Analyze the graph to find the interval(s) where the function \( f \) is concave down.
- Provide your answer using interval notation. Use the following symbols:
- \( \infty \) for infinity
- \( \cup \) for union (combining intervals)
- Parentheses \((\quad)\) for open intervals
- Brackets \([\quad]\) for closed intervals
- Enter "∅" if the interval is empty.
- Ensure that your numbers are rounded to three decimal places.
**Input Box for Interval(s):**
\[
\text{interval(s):} \underline{\hspace{8cm}}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F07bee885-b193-43d8-ac2a-8488a7e88bc2%2F6fcc5a27-afad-481e-b01d-272cde8f2447%2Fvzsfuiq_processed.png&w=3840&q=75)
Transcribed Image Text:**Instructions for Analyzing the Graph of a Function \( f \)**
1. **Finding Points of Inflection:**
- Use the graph to identify the point(s) of inflection of the function \( f \).
- Provide your answer as a comma-separated list of values in the form of exact numbers. Utilize symbolic notation and fractions where necessary.
- If the function has no inflection points, enter "DNE" (Does Not Exist).
**Input Box for Points of Inflection:**
\[
x = \underline{\hspace{3cm}}
\]
2. **Determining Intervals of Concavity:**
- Analyze the graph to find the interval(s) where the function \( f \) is concave down.
- Provide your answer using interval notation. Use the following symbols:
- \( \infty \) for infinity
- \( \cup \) for union (combining intervals)
- Parentheses \((\quad)\) for open intervals
- Brackets \([\quad]\) for closed intervals
- Enter "∅" if the interval is empty.
- Ensure that your numbers are rounded to three decimal places.
**Input Box for Interval(s):**
\[
\text{interval(s):} \underline{\hspace{8cm}}
\]
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