Max/Min Values for f(x,y,z): Lagrange Multipliers

[PhysicsMajor]

Greetings all,

Find the max and min values of
f(x,y.z)=3x-y-3z
subject to
x+y-z=0, x^(2)+2z^(2)=1

can anybody help me get this problem started.

thanks

 

[Oggy]

Just write the Lagrange function of the problem:

F(x,y,z)=3x-y-3z+\lambda_1(x+y-z)+\lambda_2(x^{2}+2z^{2}-1)

Then find the partial derivatives (they have to be 0), and solve the system of equations.

 

[dextercioby]

You'll find the critical points,though...You can't be sure which is a mex & which is a min...

Daniel.