Question about the second derivative test of a function of two variables.

Question

i understand that the second derivative test of a function of two variables uses the value of a function that utilizes $f_{xx}f_{yy}-f_{xy}^2$. I would just like to ask what conclusion would i be able to derive if $f_{xx}$ is undefined at a certain critical point.

Answer 1

Since the second derivative of $f$ is undefined at a point in the domain, it is not twice-differentiable. Therefore you may not use the second derivative test to arrive to any conclusions.