In 1691 Michel Rolle (1652?1719) first published his famous result, now widely known as "Rolle's theorem", in an obscure book on geometry and algebra, named "Methode pour resoudre les egalites." Joseph Louis Lagrange (1736-1813) and Augustin-Louis Cauchy (1789-1857) derived their mean-value theorems easily using Rolle's theorem on suitably chosen functions. The geometrical interpretations of Rolle's theorem and Lagrange's mean-value theorem are well known. In the present work, attempts have been made to generalize Rolle's theorem and thereafter to interpret the results geometrically. It turns out that Cauchy's mean-value theorem is a generalization of Rolle's theorem in the line presented here and hence its geometrical interpretation follows. In the present work, attempts have been made to generalize Rolle's theorem and thereafter to interpret the results geometrically. It turns out that Cauchy's mean-value theorem is a generalization of Rolle?s theorem in the line presented here and hence its geometrical interpretation follows.