2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/223032A result is given to find points where a real valued function on the plane is not smooth. Provided this function is induced by a smooth mapping from three dimensions to the plane, from a function on surfaces in three dimensions. This has applications to numerical methods such as image processing.Differential Geometry53C12 (Primary) 51P05, 68U10 (Secondary)text