f = (x+y+1)/Sqrt[x^2 + y^2 + 1]

gradijent = D[f,{{x,y}}]

Tacke = Solve[gradijent == 0,{x,y}]

Hodf= Simplify[D[f,{{x,y},2}]]

HodfM = MatrixForm[Hodf]

HodfuTacke = Hodf  /. Tacke

minf = Map[PositiveDefiniteMatrixQ,HodfuTacke,1]

maxf = Map[PositiveDefiniteMatrixQ,-HodfuTacke,1]

Plot3D[f,{x,-10,10},{y,-10,10},ColorFunction->Hue,PlotRange->{{-10,10},{-10,10},{-2,3}}]

Show[%100,ImageSize->Full]