In this paper we present a general approach for treating first order approximation schemes constrained extremum problems. We underline that, roughly speaking, these schemes present two geometric one and an analytical one. We will show that separation theorems and tangent fundamental role for deriving a scheme from the geometrical viewpoint; from the other derivative is the key concept for the analytical viewpoint. The purpose of the paper is scheme for first order approximations in optimization and to put in evidence the connections geometrical and analytical properties of the problem. The main interest is devoted to those which are useful for deriving necessary optimality conditions and for the construction of Solution methods.