  The three dimensional exact R symmetry of N=2 SCFTs extremizes the partition
function localized on a three sphere. Here we verify this statement at weak
coupling. We give a detailed analysis for two classes of models. The first one
is an SU(N)_k gauge theory at large k with both fundamental and adjoint matter
fields, while the second is a flavored version of the ABJ theory, where the CS
levels are large but they do not necessarily sum up to zero. We study in both
cases superpotential deformations and compute the R charges at different fixed
points. When these fixed points are connected by an RG flow we explicitly
verify that the free energy decreases at the endpoints of the flow between the
fixed points, corroborating the conjecture of an F-theorem in three dimensions.
