Question

Use Lagrange multipliers to find the maximum and minimum values (if they exist) of the temperature T(x, y, z) = 2x+6y+10z on the sphere x 2+y 2+z 2 = 35

Answer #1

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 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.

Chapter 8, Section 8.6, Question 003
Use Lagrange multipliers to find the maximum and minimum values
of f(x,y)=xy
subject to the constraint 5x+2y=60
if such values exist. Enter the exact answer. If there is no
global maximum or global minimum, enter NA.
Optimal f(x,y)=

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.

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 Lagrange multipliers to find the highest point on the curve
of intersection of the surfaces.
Sphere: x2 + y2 + z2 =
24, Plane: 2x + y − z = 2

Using Lagrange multipliers, find the coordinates of the minimum
point on the graph of z=x2+y2 subject to the constraint
2x+y=20.
Lagrange function (use k for lambda) L(x,y,k)=
Lx(x,y,k)=
Ly(x,y,k)=
Lk(x,y,k)=
Minimum Point (format (x,y,z)):

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 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 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)

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 56 seconds ago

asked 4 minutes ago

asked 6 minutes ago

asked 6 minutes ago

asked 9 minutes ago

asked 9 minutes ago

asked 9 minutes ago

asked 10 minutes ago

asked 10 minutes ago

asked 11 minutes ago

asked 11 minutes ago

asked 11 minutes ago