In a cutting insert of an embodiment of the present invention, an upper surface includes a first corner, and a second corner and a third corner respectively adjacent to both sides of the first corner. The upper surface sequentially includes a rake surface located along an upper cutting edge and inclined toward a lower surface as 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 located more inward than the rake surface and inclined toward the lower surface as 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 the minor rake surface. A cutting tool with the cutting insert, and a method of producing a machined product by using the cutting tool are also provided.