Cutting insert, cutting tool, and method for manufacturing machined product

A cutting insert comprising:

• an upper surface;
• a lower surface;
• a lateral surface located between the upper surface and the lower surface;
• and
• a cutting edge located at an intersection of the upper surface and the lateral surface,
• wherein the upper surface comprises:
• a first corner;
• a first side extending from the first corner;
• a rake face located along the first corner and the first side and approaching the lower surface as the rake face is away from the first corner and the first side;
• and
• a rising surface located along the rake face and getting away from the lower surface as the rising surface is away from the rake face,
• the rising surface comprises:
• a first recessed portion recessed with respect to the first side;
• a first protruding portion located farther from the first corner than the first recessed portion and protruding toward the first side;
• a second protruding portion located between the first protruding portion and the first side and protruding toward the first side;
• and
• a first stepped portion located between the first protruding portion and the second protruding portion,
• the first protruding portion comprises a first front end portion located closest to the first side,
• a cross section orthogonal to the first side and including the first front end portion is a first cross section, and
• at the first cross section, the second protruding portion is located closer to the lower surface than the first protruding portion.