Question

Use the method of Lagrange multipliers to set up the system of equations to find absolute maximum and minimum of the function f(x, y, z) = x^2+2y^2+3z^2 on the ellipsoid x^2 + 2y^2 + 4z^2 = 16. (Doesn't need to be solved just set up)

Answer #1

use the method of Lagrange multipliers to find the absolute
maximum and minimum values of the function subject to the given
constraints f(x,y)=x^2+y^2-2x-2y on the region x^2+y^2≤9 and
y≥0

use the method of Lagrange multipliers to find the absolute
maximum and minimum values of the function subject to the given
constraints f(x,y)=x^2+y^2-2x-2y on the region x^2+y^2≤9 and
y≥0

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.

Let f(x, y) = x 2 y 2 . Use the method of Lagrange Multipliers
to find the maximum and minimum of f on x 2 + 2y 2 = 1

The function f(x,y,z)= 4x+z^2 has an absolute maximum and
minimum values subject to the constraint of 2x^2+2y^2+3z^2=50. Use
Lagrange multipliers to find these values.

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.

The method of Lagrange multipliers assumes that the extreme
values exist, but that is not always the case. Show that the
problem of finding the minimum value of f(x,y)=x^2+y^2 subject to
the constraint xy=1 can be solved using Lagrange multipliers, but f
does not have a maximum value with that constraint.

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 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 Lagrange multipliers to find the point on the
plane
x − 2y + 3z = 6
that is closest to the point
(0, 2, 5).
(x, y, z) =

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 16 minutes ago

asked 16 minutes ago

asked 39 minutes ago

asked 45 minutes ago

asked 48 minutes ago

asked 50 minutes ago

asked 53 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago