Question

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

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 Lagrange Multipliers method to find the maximum and
minimum values of f(x,y) = xy + xz subject to the constraint x2 +y2
+ z2 = 4.

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

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...

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 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)

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.

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)=

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 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

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