Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraints. (If a value does not exist, enter NONE.)
f(x,y,z) = 3x – y – 3z;
x + y – z = 0,
x^2 + 2z^2 = 1
It is true that y does not appear in the gradient. However, after you have found, say, z as a function of x, you still have the two constraints, x+ y- z= 0 and [tex]x^2+ 2z^2= 1.
The second allows you to solve for specific values of x and z. Put those into x+ y- z= 0 to find y.