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Kernel smoothers are among the most popular nonparametric functional estimates. These estimates depend on a bandwidth that controls the smoothness of the estimate. While the literature for a bandwidth choice in a univariate density estimate is quite extensive, the progress in the multivariate case is slower. The authors focus on a bandwidth matrix selection for a bivariate kernel density estimate provided that the bandwidth matrix is diagonal. A common task is to find entries of the bandwidth matrix which minimizes the Mean Integrated Square Error (MISE). It is known that in this case there exists explicit solution of an asymptotic approximation of MISE (Wand and Jones, 1995). In the present paper we pay attention to the visualization and optimizers are presented as intersection of bivariate functional surfaces derived from this explicit solution and we develop the method based on this visualization. A simulation study compares the least square cross-validation method and the proposed method. Theoretical results are applied to real data. [ABSTRACT FROM AUTHOR]