Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
How would you find the absolute maximum and minimum values of each function over the indicated interval, and indicate the X-values at which they occur? This is for #16
![### Polynomial Functions and Their Graphs
Below are several polynomial functions along with specified intervals for analysis. A detailed explanation accompanies each graph.
#### Function 6:
- **Function:** \( f(x) = x^3 - x^2 - x + 2 \)
- **Interval:** \([-1, 2]\)
**Graph Description:**
The graph of \( f(x) = x^3 - x^2 - x + 2 \) is a cubic polynomial that shows typical features of cubic functions, such as an inflection point and turning points. The graph is plotted over the interval \([-1, 2]\), exhibiting a small oscillation with one local minimum and one local maximum within the shown range.
### Additional Functions:
7. **Function:** \( f(x) = 2x + 4 \)
- **Interval:** \([-1, 1]\)
8. **Function:** \( f(x) = 5x - 7 \)
- **Interval:** \([-2, 3]\)
9. **Function:** \( f(x) = x^2 - 6x - 3 \)
- **Interval:** \([-1, 5]\)
10. **Function:** \( f(x) = 3 - 2x - 5x^2 \)
- **Interval:** \([-3, 3]\)
11. **Function:** \( f(x) = x^3 + \frac{1}{2}x^2 - 2x + 4 \)
- **Interval:** \([-2, 0]\)
12. **Function:** \( f(x) = x^3 - x^2 - x + 3 \)
- **Interval:** \([-1, 0]\)
13. **Function:** \( f(x) = 1 + 6x - 3x^2 \)
- **Interval:** \([0, 4]\)
14. **Function:** \( f(x) = x^3 - 3x + 6 \)
- **Interval:** \([-1, 3]\)
15. **Function:** \( f(x) = x^3 - x^4 \)
- **Interval:** \([-1, 1]\)
16. **Function:** \( f(x) = x^4 - 2x^3 \)
- **Interval:**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F631ebc5c-4ef7-493e-ad4a-59361e0347ad%2Fe357e171-61a5-44d1-adb4-2bb72bdac7e4%2Fqgiavql_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Polynomial Functions and Their Graphs
Below are several polynomial functions along with specified intervals for analysis. A detailed explanation accompanies each graph.
#### Function 6:
- **Function:** \( f(x) = x^3 - x^2 - x + 2 \)
- **Interval:** \([-1, 2]\)
**Graph Description:**
The graph of \( f(x) = x^3 - x^2 - x + 2 \) is a cubic polynomial that shows typical features of cubic functions, such as an inflection point and turning points. The graph is plotted over the interval \([-1, 2]\), exhibiting a small oscillation with one local minimum and one local maximum within the shown range.
### Additional Functions:
7. **Function:** \( f(x) = 2x + 4 \)
- **Interval:** \([-1, 1]\)
8. **Function:** \( f(x) = 5x - 7 \)
- **Interval:** \([-2, 3]\)
9. **Function:** \( f(x) = x^2 - 6x - 3 \)
- **Interval:** \([-1, 5]\)
10. **Function:** \( f(x) = 3 - 2x - 5x^2 \)
- **Interval:** \([-3, 3]\)
11. **Function:** \( f(x) = x^3 + \frac{1}{2}x^2 - 2x + 4 \)
- **Interval:** \([-2, 0]\)
12. **Function:** \( f(x) = x^3 - x^2 - x + 3 \)
- **Interval:** \([-1, 0]\)
13. **Function:** \( f(x) = 1 + 6x - 3x^2 \)
- **Interval:** \([0, 4]\)
14. **Function:** \( f(x) = x^3 - 3x + 6 \)
- **Interval:** \([-1, 3]\)
15. **Function:** \( f(x) = x^3 - x^4 \)
- **Interval:** \([-1, 1]\)
16. **Function:** \( f(x) = x^4 - 2x^3 \)
- **Interval:**
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