# finding the maximum/minimum with Lagrange multipliers

• March 20th 2010, 02:24 AM
finding the maximum/minimum with Lagrange multipliers
hi i need help with finding optimum maximum/minimum of this function:

subject to these constraints:

http://i33.photobucket.com/albums/d9...dpit/const.jpg

i've got this far:

The solutions are $(1)\ x=y=\pm\sqrt{18},\ z=\pm2\sqrt{18}$ and $(2)\ x=-y=\pm\sqrt{18},\ z=0$.