<p>This paper focuses on maximal marginal functions, also known as optimal value functions, which frequently arise in variational analysis, parametric optimization, and various other fields. These functions represent the value of the objective function at the optimal solution of a maximization problem, with respect to the problem’s parameters. Generally, they are inherently nonsmooth, necessitating the use of generalized differentiation techniques for their analysis. The main results of this paper provide sufficient conditions for the tangential convexity of the marginal function and offer an upper estimate of its tangential subdifferential when this property holds. The structure of the upper estimate closely resembles results already established in the literature. Examples are included to illustrate our findings.</p>