Find the maximum and minimum values of the function
f(x,y,z)=3x−y−3z subject to the constraints x^2+2z^2=49 and
x+y−z=9. Maximum value is Maximum value is , occuring at
( , , ). Minimum value is , occuring at ( , ,
).
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
a.Find the absolute maximum and minimum for z=xy-x-y/2 over the
region bounded by y=x^2 and y=3x;
b. Find the critical points and critical values for
z=x^2+2y^2-2xy+3x+y+3.