Question

Use Lagrange Multipliers to find the extreme values of f(x,y,z)
= x^{2} + 3y subject to the constraints x^{2} +
z^{2} = 9 and 3y^{2} + 4z^{2} = 48.

Answer #1

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 the method of Lagrange multipliers to find the minimum value
of the function
f(x,y,z)=x2+y2+z2
subject to the constraints x+y=10 and 2y−z=3.

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 the method of Lagrange multipliers to find the maximum and
minimum values of F(x,y,z) = 5x+3y+4z, subject to the constraint
G(x,y,z) = x2+y2+z2 = 25. Note the
constraint is a sphere of radius 5, while the level surfaces for F
are planes. Sketch a graph showing the solution to this problem
occurs where two of these planes are tangent to the sphere.

Use the method of Lagrange Multipliers to find the maximum
value:
f(x,y,z) = x2y2z2 subject to
the constraint x2+y2+z2=1 no
decimals permitted

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.

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

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

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