I got some question about a problem I was doing.
I have to optimize $f(x,y,z) = xy + yz$, restricted to $g(x,y,z) = y^2 + z^2 = 1$, so, for Lagrange multipliers theorem, I have this:
$$ {\nabla}f = (y,x+z,y) \hspace{8mm} {\lambda}{\nabla}g = (0,2{\lambda}y,2{\lambda}z) $$
Solving for $x,y,z,{\lambda}$ I got that $(x,y,z) = (0,0,0)$, and I can't use the condition $y^2 + z^2 = 1$. Am I doing something wrong, or the function has no optimal values with that restriction?
Thanks for tour help!