Use the graph to find the point(s) of inflection of f. (Give your answer as a comma-separated list of points in the form (*, *). Use decimal notation. Give your numbers to three decimal places. Enter DNE if the function has no inflection points.) inflection point(s): Use the graph to determine the interval(s) on which the function ƒ is concave down. (Give your answer as an interval in the form (*, *). Use the symbol ∞ for infinity, u for combining intervals, and an appropriate type of parenthesis "(",")", "[",")]" depending on whether the interval is open or closed. Enter Ø if the interval is empty. Use decimal notation. Give your numbers to three decimal places.) interval(s):
Use the graph to find the point(s) of inflection of f. (Give your answer as a comma-separated list of points in the form (*, *). Use decimal notation. Give your numbers to three decimal places. Enter DNE if the function has no inflection points.) inflection point(s): Use the graph to determine the interval(s) on which the function ƒ is concave down. (Give your answer as an interval in the form (*, *). Use the symbol ∞ for infinity, u for combining intervals, and an appropriate type of parenthesis "(",")", "[",")]" depending on whether the interval is open or closed. Enter Ø if the interval is empty. Use decimal notation. Give your numbers to three decimal places.) interval(s):
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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Transcribed Image Text:**Using the graphing utility, graph the function \( y = f'(x) \).**
\( f'(x) = x^4 - 15x^3 + 73x^2 - 129x + 70 \)
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**Graph Explanation:**
The graph shows the derivative function \( f'(x) = x^4 - 15x^3 + 73x^2 - 129x + 70 \). The x-axis ranges from 0 to 8, and the y-axis ranges from -20 to 20. The curve has a smooth, continuous wave-like shape that changes direction several times, representing the critical points of the function.
- The curve rises from the left and reaches a local maximum around \( x = 3 \).
- It then falls to a local minimum slightly before \( x = 5 \).
- The curve rises sharply after \( x = 6 \).
The graph includes tools to zoom in and out and reset the view.
![**Inflection Points and Concavity Analysis**
**Instructions:**
1. **Finding Inflection Points:**
- Use the graph to identify the point(s) of inflection of the function \( f \).
- Provide your answer as a comma-separated list of points in the format \((x_1, x_2, \ldots)\).
- Use decimal notation, rounding to three decimal places.
- Enter "DNE" (Does Not Exist) if the function has no inflection points.
**Inflection point(s):** [Input box]
2. **Determining Concavity:**
- Use the graph to determine the interval(s) on which the function \( f \) is concave down.
- Provide your answer as intervals in the format \((a, b)\).
- Utilize the symbol \(\infty\) for infinity, \( \cup \) for combining intervals, and appropriate parentheses \( "(", ")", "[", "]" \) depending on whether the interval is open or closed.
- Enter \( \emptyset \) if there are no such intervals.
- Use decimal notation, rounding to three decimal places.
**Interval(s):** [Input box]
**Explanation of Graph:**
- The graph is essential for identifying where changes in concavity occur, helping locate inflection points.
- Observing the curve's shape, you can ascertain whether and where it shifts from concave up to concave down or vice versa.
Feel free to use this guide to clearly identify the key features of the function \( f \) as illustrated by the graph.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F53439359-1ad8-43a2-9307-2c193a83e82b%2F104bdedb-359e-4879-bcf0-0a3fe7bbfb41%2F1qit3w_processed.png&w=3840&q=75)
Transcribed Image Text:**Inflection Points and Concavity Analysis**
**Instructions:**
1. **Finding Inflection Points:**
- Use the graph to identify the point(s) of inflection of the function \( f \).
- Provide your answer as a comma-separated list of points in the format \((x_1, x_2, \ldots)\).
- Use decimal notation, rounding to three decimal places.
- Enter "DNE" (Does Not Exist) if the function has no inflection points.
**Inflection point(s):** [Input box]
2. **Determining Concavity:**
- Use the graph to determine the interval(s) on which the function \( f \) is concave down.
- Provide your answer as intervals in the format \((a, b)\).
- Utilize the symbol \(\infty\) for infinity, \( \cup \) for combining intervals, and appropriate parentheses \( "(", ")", "[", "]" \) depending on whether the interval is open or closed.
- Enter \( \emptyset \) if there are no such intervals.
- Use decimal notation, rounding to three decimal places.
**Interval(s):** [Input box]
**Explanation of Graph:**
- The graph is essential for identifying where changes in concavity occur, helping locate inflection points.
- Observing the curve's shape, you can ascertain whether and where it shifts from concave up to concave down or vice versa.
Feel free to use this guide to clearly identify the key features of the function \( f \) as illustrated by the graph.
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