Question

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

Answer #1

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 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 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 f(x, y,
z) = x + 2y^2 - z^2
subject to the constraint x^2 + 4y^2 + 2z^2 = 17.

Use Lagrange multipliers to find the maximum and minimum values
of f(x,y)=4x3+y2 subject to the constraint 2x2+y2=1 also, find the
points at which these extreme values occur.

Use Lagrange Multipliers to find the extreme values of f(x,y,z)
= x2 + 3y subject to the constraints x2 +
z2 = 9 and 3y2 + 4z2 = 48.

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 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.

Use Lagrange multipliers to find all relative extrema of the
function subject to the given constraint.
f(x,y)=x^2+2y^3
constraint: 2x+y^2-8=0

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

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