Question

The method of Lagrange multipliers assumes that the extreme values exist, but that is not always the case. Show that the problem of finding the minimum value of f(x,y)=x^2+y^2 subject to the constraint xy=1 can be solved using Lagrange multipliers, but f does not have a maximum value with that constraint.

Answer #1

Use the method of Lagrange multipliers to find the extreme
values of f(x,y)=
x^(2) + y^(2) − xy − 4 subject to the constraint x + y = 6.

Use the method of Lagrange Multipliers to find the extreme
value(s) of f(x, y) = 3x + 2y subject to the constraint y = 3x ^2 .
Identify the extremum/extrema as maximum or minimum.

Use the Lagrange Multipliers method to find the maximum and
minimum values of f(x,y) = xy + xz subject to the constraint x2 +y2
+ z2 = 4.

f(x,y)=xy ; 4x^2+y^2=8
Use Lagrange multipliers to find the extreme values of the
function subject to the given constraint.

Use Lagrange multipliers to find the maximum and minimum values
of
f(x,y)=xy
subject to the constraint 25x^2+y^2=200
if such values exist.
Enter the exact answers. Which is global maximum/global minimum?
Enter NA in the appropriate answer area if these do not apply.

Chapter 8, Section 8.6, Question 003
Use Lagrange multipliers to find the maximum and minimum values
of f(x,y)=xy
subject to the constraint 5x+2y=60
if such values exist. Enter the exact answer. If there is no
global maximum or global minimum, enter NA.
Optimal f(x,y)=

Use the lagrange multipliers to find the maximum or minimum
value if it exist F(x,y) -xyz subject to the constraint x+y+z=3

Use Lagrange multipliers to find the maximum and minimum values
of f(x,y)=x2+5y
subject to the constraint x2-y2=3 , if
such values exist.
Maximum =
Minimum

Use the method of Lagrange multipliers to find the maximum value
of f(x,y) = xy subject to the constraint x^2=y^2=7 (you may assume
that the extremum exists)

Use Lagrange Multipliers to find the extreme values of f(x, y,
z) = x + 2y^2 - z^2
subject to the constraint x^2 + 4y^2 + 2z^2 = 17.

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