About differentiability of order one of quasiconvex functions onRn

This paper is devoted to the study of the different kinds of differentiability of quasiconvex functions onRn. For these functions, we show that Gâteaux-differentiability and Fréchet-differentiability are equivalent; we study the properties of the directional derivatives; and we show that if, for a quasiconvex function, the directional derivatives atx are all finite and two-sided, the function is differentiable atx.