59-62 Use Lagrange multipliers to find the maximum and minimum values of f subject to the given constraint(s). 59. f(x, y) = x²y; x² + y² = 1 1 = - X 60. f(x, y) = + 1 ; 1 x² + 1 2 y² - 2 1 y 1000 61. f(x, y, z) = xyz; x² + y² + z² = 3 bruoa io basa J
59-62 Use Lagrange multipliers to find the maximum and minimum values of f subject to the given constraint(s). 59. f(x, y) = x²y; x² + y² = 1 1 = - X 60. f(x, y) = + 1 ; 1 x² + 1 2 y² - 2 1 y 1000 61. f(x, y, z) = xyz; x² + y² + z² = 3 bruoa io basa J
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
61
Transcribed Image Text:ost
alue
ad,
57. Use a graph or level curves or both to estimate the local
maximum and minimum values and saddle points of
f(x, y) = x³ - 3x + y4 - 2y2. Then use calculus to find
these values precisely.
58. Use a graphing calculator or computer (or Newton's method
or a computer algebra system) to find the critical points of
f(x, y) = 12 + 10y - 2x²
2x² - 8xy - y correct to three
decimal places. Then classify the critical points and find
the highest point on the graph.
59-62 Use Lagrange multipliers to find the maximum and
minimum values of f subject to the given constraint(s).
59. f(x, y) = x²y;
60. f(x, y) =
x²y; x² + y
+ y² = 1
1
+
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61. f(x, y, z) = xyz; x² + y² + z² = 3
62. f(x, y, z) = x² + 2y² + 3z²;
event bruoa jo boup of Al
Antaquanto all
nottanut odi yd bols
x+y+z= 1, xy + 2z = 2
3
10
63. Find the points on the surface xy²z³ = 2 that are closest to
the origin.
anDis
CONTACT
64. A package in the shape of a rectangular box can be mailed by
the US Postal Service if the sum of its length and girth (the
perimeter of a cross-section perpendicular to the length) is at
most 108 in. Find the dimensions of the package with largest
volume that can be mailed.
ADE
001
a
65. A pentagon is formed by placing an isosceles triangle c
rectangle, as shown in the figure. If the pentagon has fixed
that
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