Question

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.

Answer #1

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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 the method of Lagrange multipliers to find the maximum value
of f subject to the given constraint. f(x,y)=−3x^2−4y^2+4xy,
subject to 3x+4y+528=0

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 Lagrange multipliers to find the
extreme values of subject to the given constraint
3x+y; x^2 + y^2 = 1

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.

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.

1. Use the method of Lagrange multipliers to find the
maximize
of the function f (x, y) = 25-x^2-y^2 subject to the constraint
x + y =-1
2. Use the method of Lagrange multipliers to find the
minimum
of the function f (x, y) = y^2+6x subject to the constraint
y-2x= 0

Use Lagrange multipliers to find both the maximum and minimum of
the function f(x, y) = 3x + 4y subject to the constraint that the
point be on the circle x 2 + y 2 = 100.

Use the method of Lagrange Multipliers to find the maximum value
of the function f(x,y)= x^3y^2 subject to the constraint
x^2+y^2=10.

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.

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