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}.
1. Find absolute max and min of f(x,y)=
x^2- xy + y^2 +1 on the closed triangular plate in the first
quadrant x=0, y=4, y=x
2. Given position of a particle by π (t)= Cos2ti + 3
sin2ti, Find the
particle velocity and acceleration at t=0
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