4. The function has a maximum and minimum extreme value. Use Lagrange multipliers to find the extreme values of the function subject to the given constraint. f(x,y) = x² + y² + z², xyz = 4
4. The function has a maximum and minimum extreme value. Use Lagrange multipliers to find the extreme values of the function subject to the given constraint. f(x,y) = x² + y² + z², xyz = 4
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Expert Solution
Step 1
Given and constraint
Let
where is the lagrange multiplier.
Step 2
Solving by multiplying both sides of the equation (1), (2) and (3) by x, y and z respectively,
Equating,
Substituting back to the constrained equation,
Step by step
Solved in 3 steps
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