data=BlockRandom[SeedRandom[100];
RandomVariate[WeibullDistribution[4,5],50]];

params=FindDistributionParameters[data,WeibullDistribution[α,β]];

llfun=LogLikelihood[WeibullDistribution[α,β],data];
cp=Show[ContourPlot[llfun,{α,2,6},{β,3,8},Contours->20,ColorFunction->"FallColors"],Graphics[Point[{α,β}/.params]]];
p3d=Show[Plot3D[llfun,{α,2,6},{β,3,8},MeshFunctions->{#3&},Mesh->20,PlotPoints->50,ColorFunction->"FallColors"],Graphics3D[{Black,Sphere[{α,β,llfun}/.params,.05]}]];
GraphicsRow[{cp,p3d}]