b. In the first equation, diminishing returns occurs at 10 units of output, the point at which MC reaches its minimum point.
In the second equation, diminishing returns begins immediately after production starts.
In the third equation, diminishing returns does not occur over the range of output being considered.
In the first and second equations, the point of minimum average cost occurs at the point at which MC intersects the AC curve (i.e. approximately 17 and 6, respectively). The minimum point is never actually reached in the case of the third equation.
c. Students should simply observe how the MC intersects the AVC and AC lines at their minimum points in the cubic equation; how MC is always above AVC in the quadratic equation, and how MC is actually equal to AVC and never quite intersects the AC line in the case of the linear equation.