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
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 f(x, y, z) = x^2yz^2
subject to the constraint 2x ^2 + 3y^ 2 + 6z^ 2 = 33
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 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