Use the graph to answer the following questions.
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
![**Objective Knowledge Check**
**Question 4**
Below is the graph of a polynomial function with real coefficients. All local extrema of the function are shown in the graph.
[Graph of a polynomial]
**Description of the Graph:**
The graph shows a polynomial curve with fluctuations, having local maxima and minima. The x-axis is marked at intervals with values such as -6, -4, -2, 0, 2, 4, 6, etc., and the y-axis is marked similarly. The curve intersects the x-axis multiple times and has noticeable peaks and valleys.
**Use the graph to answer the following questions.**
(a) Over which intervals is the function increasing? Choose all that apply.
- \((-∞, -2)\)
- \((-2, 0)\)
- \((0, 3)\)
- \((3, 5)\)
- \((3, 7)\)
- \((7, ∞)\)
(b) At which x-values does the function have local minima? If there is more than one value, separate them with commas.
(c) What is the sign of the function's leading coefficient?
- (Choose one)
(d) Which of the following is a possibility for the degree of the function? Choose all that apply.
- 4
- 5
- 6
- 7
- 8
- 9
[Options for submitting answers and navigation buttons are present below the questions.]
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Transcribed Image Text:**Objective Knowledge Check**
**Question 4**
Below is the graph of a polynomial function with real coefficients. All local extrema of the function are shown in the graph.
[Graph of a polynomial]
**Description of the Graph:**
The graph shows a polynomial curve with fluctuations, having local maxima and minima. The x-axis is marked at intervals with values such as -6, -4, -2, 0, 2, 4, 6, etc., and the y-axis is marked similarly. The curve intersects the x-axis multiple times and has noticeable peaks and valleys.
**Use the graph to answer the following questions.**
(a) Over which intervals is the function increasing? Choose all that apply.
- \((-∞, -2)\)
- \((-2, 0)\)
- \((0, 3)\)
- \((3, 5)\)
- \((3, 7)\)
- \((7, ∞)\)
(b) At which x-values does the function have local minima? If there is more than one value, separate them with commas.
(c) What is the sign of the function's leading coefficient?
- (Choose one)
(d) Which of the following is a possibility for the degree of the function? Choose all that apply.
- 4
- 5
- 6
- 7
- 8
- 9
[Options for submitting answers and navigation buttons are present below the questions.]
© 2021 McGraw Hill LLC. All Rights Reserved.
Expert Solution
Step 1
Consider the given graph as,
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