The embedding theory of spaces of differential functions of many variables studies important connections and relationships between smooth and metric properties of functions and has wide application in various branches of pure mathematics and its applications. Earlier, we obtained the embedding theorems of different metrics for Nikolsky-Besov spaces with dominant mixed smoothness and mixed smoothness and mixed metric, and anisotropic Lorentz spaces. In this work, we showed that the conditions for the parameters of spaces from the theorems are unimprovable. To do this, we built the extreme functions included in the spaces from the left sides of the embeddings and not included in the "slightly narrowed" spaces from the spaces in the right parts of the embeddings.