Which of these points are local minima? □ (-√2,-1) (-√2,1) (√2,-1) (√2, 1) □ (√2,0) □ (-√2,0)

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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?(?,?)= x^3+y^4−6x−2y^2+2

### Which of these points are local minima?

Please review the list of points below. Determine which of these points are local minima:

- [ ] \((- \sqrt{2}, -1)\)
- [ ] \((- \sqrt{2}, 1)\)
- [ ] \((\sqrt{2}, -1)\)
- [ ] \((\sqrt{2}, 1)\)
- [ ] \((\sqrt{2}, 0)\)
- [ ] \((- \sqrt{2}, 0)\)
Transcribed Image Text:### Which of these points are local minima? Please review the list of points below. Determine which of these points are local minima: - [ ] \((- \sqrt{2}, -1)\) - [ ] \((- \sqrt{2}, 1)\) - [ ] \((\sqrt{2}, -1)\) - [ ] \((\sqrt{2}, 1)\) - [ ] \((\sqrt{2}, 0)\) - [ ] \((- \sqrt{2}, 0)\)
### Educational Math Quiz

#### Question: Which point is a local maximum?

- ○ \((- \sqrt{2}, 1)\)
- ○ \((- \sqrt{2}, -1)\)
- ○ \((\sqrt{2}, 1)\)
- ○ \((\sqrt{2}, -1)\)
- ○ \((- \sqrt{2}, 0)\)
- ○ \((\sqrt{2}, 0)\)

In this multiple-choice question, you're asked to identify which of the given points represents a local maximum. A local maximum occurs at a point on a graph where the function changes from increasing to decreasing, creating a peak. Select the correct option based on your analysis.

There are no graphs or diagrams provided in this question.
Transcribed Image Text:### Educational Math Quiz #### Question: Which point is a local maximum? - ○ \((- \sqrt{2}, 1)\) - ○ \((- \sqrt{2}, -1)\) - ○ \((\sqrt{2}, 1)\) - ○ \((\sqrt{2}, -1)\) - ○ \((- \sqrt{2}, 0)\) - ○ \((\sqrt{2}, 0)\) In this multiple-choice question, you're asked to identify which of the given points represents a local maximum. A local maximum occurs at a point on a graph where the function changes from increasing to decreasing, creating a peak. Select the correct option based on your analysis. There are no graphs or diagrams provided in this question.
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