on the region f(x, y, z)=x²-2y + y² + ²² +2 M = {(x, y, z): ² + y² + 2² ≤ 4}. a) Find the critical points of f inside M and classify them as local min, local max or saddle pt. b) Now find the maximum and minimum values of f on the portion of M on the xy plane. This is the equator disk: S= {(z,y.0): ² + y² ≤ 4}, whose boundary S is a circle of a radius 2. c) Now use the method of Lagrange multipliers to find the maximum and minimum values off in the wwhole region M, listing all points at which those values occur. Note: feel free to use a calculator for part (c). If you use decimal expansion for the numbers, please use 3 decimal places.
on the region f(x, y, z)=x²-2y + y² + ²² +2 M = {(x, y, z): ² + y² + 2² ≤ 4}. a) Find the critical points of f inside M and classify them as local min, local max or saddle pt. b) Now find the maximum and minimum values of f on the portion of M on the xy plane. This is the equator disk: S= {(z,y.0): ² + y² ≤ 4}, whose boundary S is a circle of a radius 2. c) Now use the method of Lagrange multipliers to find the maximum and minimum values off in the wwhole region M, listing all points at which those values occur. Note: feel free to use a calculator for part (c). If you use decimal expansion for the numbers, please use 3 decimal places.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 78E
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Transcribed Image Text:ture.com/courses/1337195/assignments/5867675
(4) Consider the scalar function
on the region
f(x, y, z)=x²-2y+yz+z²+2
M = {(x, y, z): 2² + y² + 2² ≤ 4}.
(a) Find the critical points of f inside M and classify them as local min, local max or saddle pt.
(b) Now find the maximum and minimum values of f on the portion of M on the xy plane. This is the
equator disk:
S= {(x, y,0): a² + y² ≤ 4},
whose boundary OS is a circle of a radius 2.
(c) Now use the method of Lagrange multipliers to find the maximum and minimum values of f in the
whole region M, listing all points at which those values occur.
Note: feel free to use a calculator for part (c). If you use decimal expansion for the numbers, please use 3.
decimal places.
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