Answer
Local minimum by second derivative test
Work Step by Step
first compute D = f_{xx}(1,1)f_{yy}(1,1)-[f_{xy}(1,1)]^{2}
(4)(2)-(1)^{2}=7
since D(1,1)>0 we check f_{xx}(1,1)
f_{xx}(1,1)=4>0
so since D(1,1)>0 and f_{xx}(1,1)> 0 , f has a local minimum at (1,1) by the second derivative test
