a.)
Find the shortest distance from the point (0,1,2) to any point
on the plane x - 2y +z = 2 by finding the function to optimize,
finding its critical points and test for extreme values using the
second derivative test.
b.)
Write the point on the plane whose distance to the point (0,1,2)
is the shortest distance found in part a) above. All the work
necessary to identify this point would be in part a). You just need
to...
Starting from the point (x0, y0) = (2,3) of the function f (x) =
4x ^ 2 - 4xy + 2y ^ 2, it is to choose to proceed according to the
Steep Descent Method (x2, y2).
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
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