Max and min values of $f(x,y,z) = yz+xy$ subject to $y^2 +z^2 = 289$ and $xy =5$.
I know this will be a LaGrange problem and two constraints will be utilized so the formula you're looking for is the gradient of f(x,y,z) equal to the gradient of each constraint. Then it's a process of solving for x,y,z and the two associated variables with the constraints (say lamda and upsilon).
However, if you were to take the gradient of $f(x)$ you'll get $0 = 0 + uy$, won't you? This seems like a pretty standard question, and I think I understand the overall process, but I'm a bit uncertain of how to isolate variables in this case.