Question

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.

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.

Using Lagrange multipliers
Minimize f(x,y,z)=x^2+4y^2+2z^2
subject to x+2y+z=10

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 extremal values of
f(x,y,z)=2x+2y+z subject to the
constraint
x2+y2+z2=9.

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

use lagrange multipliers to locate the maximum of f(x,y,z) =
2x^2 - 2y + z^2 subject to the constraint x^2 + y^2 + z^2 = 1

Use Lagrange multipliers to find the minimum value of f ( x , y
, z ) = 2 x 2 + y 2 + 3 z 2 subject to the constraint 2 x − 3 y − 4
z = 49. The minimum value of f ( x , y ) subject to 2 x − 3 y − 4 z
= 49 is

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.

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