use Lagrange multipliers to find the maximum and minimum values
of f subject to the given...
use Lagrange multipliers to find the maximum and minimum values
of f subject to the given constraint, if such values
exist. f(x, y, z) =
xyz, x2 + y2 +
4z2 = 12
Use Lagrange multipliers to find the minimum and maximum values
for the following functions subject to the given constaints.
a) f(x,y) = 8x2+y2 ; x4+y4
= 4
b) f(x,y,z) = 2z-8x2 ;
4x2+y2+z2 = 1
c) f(x,y,z) = xyz ; x2+4y2+3z2
= 36
Use the method of Lagrange multipliers to find the absolute
maximum and minimum values of the function f(x, y, z) = x^2yz^2
subject to the constraint 2x ^2 + 3y^ 2 + 6z^ 2 = 33
2.) Use the method of Lagrange multipliers to find the
maximum and minimum values of the function ?(?, ?) = ??^2 − 2??^2
given the constraint ?^2 + ?^2 = 2 along with evaluating the
critical points of the function, find the absolute extrema of the
function ?(?, ?) = ??^2 − 2??^2 in the region ? = {(?, ?)|?^2 + ?^2
≤ 2}.
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
Find the maximum and minimum values of f subject to the
given constraints. Use a computer algebra system to solve the
system of equations that arises in using Lagrange multipliers. (If
your CAS finds only one solution, you may need to use additional
commands. Round your answer to four decimal places.)
f(x, y,
z) = yex
−
z; 9x2
+ 4y2 +
36z2 =
36, xy + yz = 1
Use Lagrange multipliers to solve the given optimization
problem. HINT [See Example 2.] Find the minimum value of f(x, y) =
x2 + y2 subject to x + 2y = 45.
fmin =
Also find the corresponding point (x, y). (x, y) =