Question

what is the Maximum and minimum of the
f(x,y,z)=(xy+z)/(z^2+1)
in the{(x,y,z):z>=0,x^2+y^2<=1

Answer 1

Global minimum at {x -> 1/Sqrt[2], y -> -(1/Sqrt[2]), z -> 0} valued - 1/2

Answer 2

Global maximum (this one I am not sure) at {x -> -Sqrt[
2] (1/2 (1 - Sqrt[5]) - 1/16 (-1 - Sqrt[5]) (-1 + Sqrt[5])^2 +
1/4 (1 + Sqrt[5])), y -> -(1/Sqrt[2]), z -> 1/2 (-1 + Sqrt[5])}, valued 1/4 (1 + Sqrt[5])