39 (Baker No. 542) Surface with unique local extremum but no global extremum
This illustrates an interesting fact in multivariable calculus, that it is possible to have a function of two variables with a critical point that is not a local minimum, despite its being a minimum for all one-dimensional sections. “Peano. The surface z = (y^2 - ax)( y^2 - bx) has all normal sections at the origin with a minimum but the surface without.” |