Question

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.

Answer #1

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)

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 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 Lagrange multipliers to find the maximum value of the
function f(x,y) = xy given the constraint x+y=10

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 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 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 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 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 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

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