Question

Solve the following problems by USING Lagrange multipliers.

(a) Find the maximum and minimum values of f(x, y, z) = x^2 + y^2 + z^2 subject to the constraint (x − 1)^2 + (y − 2)^2 + (z − 3)^2 = 4

(b) Find the maximum and minimum values of f(x, y, z) = x^2 + y^2 + z^2 subject to the constraints (x − 1)^2 + (y − 2)^2 + (z − 3)^2 = 9 and x − 2z = 0.

Answer #1

THUMB UP PLEASE

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 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 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 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 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 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)=

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