e38bdd3c-... 1 fcf9c8b-49a3-3a60-a674-6d0f56462f50 Not Secure courses1.webwork.maa.org:8080/wwtmp... * WeBWork : creighton-math23 x + IncreasingDecreasingConcaveConvex/5/ 1. Find the open interval(s) on which f is concave upward. Answer (in interval notation): (0,2)U(5,8) 2. Find the open interval(s) on which f is concave downward. Answer (in interval notation): (2,4)U(4,5) 3. Find the coordinates of the points of inflection. List your answers as points in the form (a, b). Answer (separate by commas): (2,5).(4,5).(5,5) Note: You can click on the graph to enlarge the image.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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### Calculus Exercise: Concavity and Points of Inflection

#### Instructions

1. **Determine Intervals of Concavity:**
   - **Concave Upwards:**
     - **Task:** Find the open interval(s) on which the graph is concave upwards.
     - **Answer Format:** Provide your answer in interval notation. Example: (0, 2) ∪ (5, 8).

   - **Concave Downwards:**
     - **Task:** Find the open interval(s) on which the graph is concave downwards.
     - **Answer Format:** Provide your answer in interval notation. Example: (2, 4) ∪ (4, 5).

2. **Identify Points of Inflection:**
   - **Task:** Find the coordinates of the points of inflection.
   - **Answer Format:** Separate coordinates using commas. Example: (2, 5), (4, 5), (5, 5).

#### Visual Representation

The graph below illustrates the function with its concavity changes and points of inflection. 

- The graph has a curve with varying concavity: 
  - It starts with an upward concave section, transitions into a downward concave section, and then returns to upward concavity.

#### Interactive Note

You can click on the graph to enlarge the image for a better view of its features and details.

**Note:** Always refer to your calculus textbook or class notes to verify these graphical interpretations and understand the theoretical basis behind concavity and points of inflection.
Transcribed Image Text:### Calculus Exercise: Concavity and Points of Inflection #### Instructions 1. **Determine Intervals of Concavity:** - **Concave Upwards:** - **Task:** Find the open interval(s) on which the graph is concave upwards. - **Answer Format:** Provide your answer in interval notation. Example: (0, 2) ∪ (5, 8). - **Concave Downwards:** - **Task:** Find the open interval(s) on which the graph is concave downwards. - **Answer Format:** Provide your answer in interval notation. Example: (2, 4) ∪ (4, 5). 2. **Identify Points of Inflection:** - **Task:** Find the coordinates of the points of inflection. - **Answer Format:** Separate coordinates using commas. Example: (2, 5), (4, 5), (5, 5). #### Visual Representation The graph below illustrates the function with its concavity changes and points of inflection. - The graph has a curve with varying concavity: - It starts with an upward concave section, transitions into a downward concave section, and then returns to upward concavity. #### Interactive Note You can click on the graph to enlarge the image for a better view of its features and details. **Note:** Always refer to your calculus textbook or class notes to verify these graphical interpretations and understand the theoretical basis behind concavity and points of inflection.
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