Peano Surface

The function

$$f(x,y)=(2x^2-y)(y-x^2)$$

which does not have a Local Maximum at (0, 0), despite criteria commonly touted in the second half of the 1800s which indicated the contrary.

See also Local Maximum

References

Fischer, G. (Ed.). Plate 122 in Mathematische Modelle/Mathematical Models, Bildband/Photograph Volume. Braunschweig, Germany: Vieweg, p. 119, 1986.

Leitere, J. ``Functions.'' §7.1.2 in Mathematical Models from the Collections of Universities and Museums (Ed. G. Fischer). Braunschweig, Germany: Vieweg, pp. 70-71, 1986.