17. f (1,y, z) = x subject to z? + y? + 2² – z = 1 %3D
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
Section 12.9 - Lagrange Multipliers Number 17
![17. f (x, y, 2) = x subject to r? + y? + 2 – z = 1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F09613d8c-4cef-4639-a65c-ee2add319cba%2Ff0c4cb83-903b-479e-9266-2009b7d9b46d%2Fehsqaz8_processed.png&w=3840&q=75)
Transcribed Image Text:17. f (x, y, 2) = x subject to r? + y? + 2 – z = 1
![15-24. Lagrange multipliers in three variables Use Lagrange multipliers to find the maximum and minimum values of
f (when they exist) subject to the given constraint.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F09613d8c-4cef-4639-a65c-ee2add319cba%2Ff0c4cb83-903b-479e-9266-2009b7d9b46d%2F4s5benk_processed.png&w=3840&q=75)
Transcribed Image Text:15-24. Lagrange multipliers in three variables Use Lagrange multipliers to find the maximum and minimum values of
f (when they exist) subject to the given constraint.
Expert Solution
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Step 1
Let . We now have . Let be the lagrnage's multiplier. Then we have implying that .
We also have the relation .
We now have
Solving the above relations, we get .
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