Question

Use Lagrange multipliers to find the maximum and minimum values
of f(x,y)=x^{2}+5y

subject to the constraint x^{2}-y^{2}=3 , if
such values exist.

Maximum = | |

Minimum |

Answer #1

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 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)=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 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 to find the maximum or minimum
value if it exist F(x,y) -xyz subject to the constraint x+y+z=3

Use Lagrange Multipliers to find both the maximum and minimum
values of f(x, y) = 4xy subject to the constraint x^2 + y^2 =
2.

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

Use Lagrange multipliers to find the maximum and minimum values
of f(x,y)=6x+y on the ellipse x2+16y2=1

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.

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