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Find the global maximum and minimum of (2x-y+32)e²+²+² f(x, y, z) = on A = {(x, y, z) € R³ x² + y² + ² ≤ 14}.

Find the global maximum and minimum of (2x-y+32)e²+²+² f(x, y, z) = on A = {(x, y, z) € R³ x² + y² + ² ≤ 14}.

Advanced Engineering Mathematics
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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Find the global maximum and minimum of f(x, y, z) = (2x -y + 32) ²²+₁²+1² on A = {(x, y, z) € R³ x² + y² + 2² ≤ 14}.
Transcribed Image Text:Find the global maximum and minimum of f(x, y, z) = (2x -y + 32) ²²+₁²+1² on A = {(x, y, z) € R³ x² + y² + 2² ≤ 14}.
Expert Solution
Step 1

Find the global maximum and minimum of fx,y,z=2x-y+3zex2+y2+z22

on A=x,y,z∈ℝ3| x2+y2+z2≤14

Solution:

Here, maximum value of ex2+y2+z22 on A is

ex2+y2+z22=e142                    =e7

Now, we have to find the global minimum and maximum of 2x-y+3z on A.

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