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

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- Feb 23rd 2010, 05:25 PMsammygirl2791Use Lagrange multipliers to find the maximum and minimum
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 - Feb 23rd 2010, 05:41 PMpickslides
- Feb 23rd 2010, 05:49 PMsammygirl2791
I can' figure out how to find y

- Feb 23rd 2010, 07:25 PMpickslides
- Feb 24th 2010, 02:40 AMHallsofIvy
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.