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

A cutting insert, comprising:

• an upper surface;
• a lower surface located on an opposite side of the upper surface;
• a lateral surface connected to the upper surface and the lower surface;
• a upper cutting edge located on an intersection between the upper surface and the lateral surface;
• and
• a lower cutting edge located on an intersection between the lower surface and the lateral surface, wherein
• the upper surface comprises
• a first corner,
• a first side connected to the first corner, and
• a second side connected to the first corner on an opposite side of the first side,
• the upper cutting edge comprises
• a main cutting edge located on the first side and having a linear shape in a top view,
• a minor cutting edge located on the second side and having a linear shape in the top view, and
• a connection edge located on the first corner, connected to the main cutting edge and the minor cutting edge, and having a protruding curved shape protruding outward in the top view,
• the minor cutting edge has a protruding curved shape protruding upward in a side view and comprises
• a first portion comprising an apex portion protruding most upward in the minor cutting edge,
• a second portion located between the first portion and the connection edge, and
• a third portion located between the second portion and the connection edge,
• each of the second portion and the third portion comes close to the lower surface with distance from the first portion, and
• in the side view, a radius of curvature of the second portion is larger than a radius of curvature of the first portion and a radius of curvature of the third portion.