Answer
True
Work Step by Step
Let $f$ be a function of two variables with continuous second-order partial derivatives in some disk centered at a critical point $\left(x_{0}, y_{0}\right),$ and let
\[
f_{x x}\left(x_{0}, y_{0}\right) f_{y y}\left(x_{0}, y_{0}\right)-f_{x y}^{2}\left(x_{0}, y_{0}\right)=D
\]
$[a]$ If $D>0$ and $f_{x x}\left(x_{0}, y_{0}\right)>0,$ then $f$ has a relative minimum at $\left(x_{0}, y_{0}\right)$
$[b]$ If $D>0$ and $f_{x x}\left(x_{0}, y_{0}\right)<0,$ then $f$ has a relative maximum at $\left(x_{0}, y_{0}\right)$
So we can directly conclude that if $D>0,$ then there will be relative extremum at $\left(x_{0}, y_{0}\right)$
