Let $f:\mathbb{R}^{2}\rightarrow\mathbb{R}$ be a smooth function with positive definite Hassian at every . Let $(a,b)\in\mathbb{R}^{2}$ be a critical point of $f$ then
$A.$ $f$ has global minimum at $(a,b).$
$B.$ $f$ has a local , but not global minimum at $(a,b).$
$C.$ $f$ has a local, but not global maximum at $(a,b).$
$D.$ $f$ has a global maximum at $(a,b).$
I only know that if Hassian matrix is positive definite definite at $(a,b)$ then it is a point of local minimum. Now what about global minimum? Please help me. Thanks a lot.