It appears z= f(x,y) has a global max/min at another particular (x,y). Using only one
independent variable $x$ at fixed $y$ i.e., for z = f(x) I get another max/min point
for $x$ optimum point location.
Max[f(x)] in 2D-space is way different compared to max[f(x,y)] in 3D-space.
I am searching for some article or textbook supporting this intuition.
Could you recommend any relevant literature for me so I can go from normal derivatives
to using partial derivatives in finding extrema? Thanks in advance!