Show that

$\displaystyle

\Delta=f_{xx}f_{yy}-(f_{xy})^2

$

is zero at the origin. Then classify this critical point by visualizing the surface

$\displaystyle

f(x, y) = x^3 + y^3

$

I have proved the first condition, but I am not sure how to proceed with the second part to classify this critical point by visualizing the surface.

Any help will be greatly appreciated!