Use Lagrange multiplier techniques to find the local extreme values of the given function subject to the stated constraint. If appropriate, determine if the extrema are global. (If a local or global extreme value does not exist enter DNE.) f(x, y) = 5x + y + 3 with constraint g(x, y) = xy 1 3+2√5 x not global ✔✔ -2√5 +3 x local max local min not global ✔
Use Lagrange multiplier techniques to find the local extreme values of the given function subject to the stated constraint. If appropriate, determine if the extrema are global. (If a local or global extreme value does not exist enter DNE.) f(x, y) = 5x + y + 3 with constraint g(x, y) = xy 1 3+2√5 x not global ✔✔ -2√5 +3 x local max local min not global ✔
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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i got positive 2 square root of 5 plus three and negative 2 square root of 5 plus 3 but its wrong
![**Title:** Using Lagrange Multiplier Techniques for Finding Extreme Values
**Instruction:** Use Lagrange multiplier techniques to find the local extreme values of the given function subject to the stated constraint. If appropriate, determine if the extrema are global. (If a local or global extreme value does not exist, enter NONE.)
**Function:**
\[ f(x, y) = 5x + y + 3 \]
**Constraint:**
\[ g(x, y) = xy - 1 \]
**Results:**
- **Local Maximum**
- Value: \( 3 + 2\sqrt{5} \)
- Global Status: Selected as "not global."
- Result: Incorrect (marked with a red "X").
- **Local Minimum**
- Value: \(-2\sqrt{5} + 3 \)
- Global Status: Correctly marked as "not global" with a green check mark.
- Result: Correct (marked with a green check mark).
**Explanation:**
This exercise involves using Lagrange multipliers to determine the local extrema for a given function with a specific constraint. The goal is to ascertain whether these extrema are also global within the given constraint. Each solution provides a calculated local maximum or minimum value, and a selection of its global status, with immediate feedback on accuracy.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F02af43a5-a1ff-44d9-89dd-1e2db9d95d08%2F8e06e97e-06cc-4764-add3-02ff778ca0f7%2Fe5i3s1_processed.png&w=3840&q=75)
Transcribed Image Text:**Title:** Using Lagrange Multiplier Techniques for Finding Extreme Values
**Instruction:** Use Lagrange multiplier techniques to find the local extreme values of the given function subject to the stated constraint. If appropriate, determine if the extrema are global. (If a local or global extreme value does not exist, enter NONE.)
**Function:**
\[ f(x, y) = 5x + y + 3 \]
**Constraint:**
\[ g(x, y) = xy - 1 \]
**Results:**
- **Local Maximum**
- Value: \( 3 + 2\sqrt{5} \)
- Global Status: Selected as "not global."
- Result: Incorrect (marked with a red "X").
- **Local Minimum**
- Value: \(-2\sqrt{5} + 3 \)
- Global Status: Correctly marked as "not global" with a green check mark.
- Result: Correct (marked with a green check mark).
**Explanation:**
This exercise involves using Lagrange multipliers to determine the local extrema for a given function with a specific constraint. The goal is to ascertain whether these extrema are also global within the given constraint. Each solution provides a calculated local maximum or minimum value, and a selection of its global status, with immediate feedback on accuracy.
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