function is concave up at (-1, 6), concave down at (7, -4), and has an inflection point at (3,1). Sketch the graph.. Submit handwritten work in Canvas.
function is concave up at (-1, 6), concave down at (7, -4), and has an inflection point at (3,1). Sketch the graph.. Submit handwritten work in Canvas.
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:### Problem Statement:
A function is concave up at (-1, 6), concave down at (7, -4), and has an inflection point at (3,1). Sketch the graph.
### Submission Instructions:
- Submit handwritten work in Canvas.
### Explanation:
For this problem, you are asked to sketch a graph based on the given properties of the function:
1. **Concave Up at (-1, 6)**: This means the graph of the function is "U-shaped" and opens upwards around the point (-1, 6).
2. **Concave Down at (7, -4)**: This implies that the function is "n-shaped" and opens downwards around the point (7, -4).
3. **Inflection Point at (3, 1)**: An inflection point is where the graph changes concavity. At (3, 1), the function changes its curvature from concave up to concave down, or vice versa.
Use these properties to sketch a graph that accurately represents the function. Your graph should reflect the changes in concavity and include the inflection point.
### Note:
Please make sure to clearly mark the points of concavity and the inflection point on your graph for clarity. Follow the instruction to submit your handwritten work in Canvas.
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