A cutting insert comprises an upper surface including a first corner, and a second and third corner, respectively, adjacent to both sides of the first corner. The upper surface sequentially includes a rake surface along an upper cutting edge, inclined toward a lower surface, going inward from the upper cutting edge at a rake angle on a basis of a perpendicular plane perpendicular to a central axis extending between the upper and lower surfaces, and a connection surface more inward than the rake surface, inclined toward the lower surface, going inward at a connection angle on the basis of the perpendicular plane. An intersecting part of the rake surface and the connection surface includes a highest position in a portion of the intersecting part corresponding to a minor rake surface. A cutting tool with cutting insert, and a method of producing a machined product using the cutting tool are provided.