This question relies on the fundamental differential relationships between load, shear force (V) and bending moment (M) along a beam. For a beam carrying a distributed load intensity w:

• dV/dx = −w — the slope of the shear-force diagram equals the (negative of) the load intensity.
• dM/dx = V — the slope of the bending-moment diagram equals the shear force at that section.

From calculus, the bending moment M reaches a maximum or minimum (a turning point) where its slope is zero, i.e. where dM/dx = 0. Because dM/dx = V, this condition becomes:

V = 0 → M is maximum (or minimum)

So the maximum bending moment occurs at the section where the shear force = 0, which on the shear-force diagram is exactly the point where the SFD crosses the zero (base) line. For a beam with several point loads, the SFD is a series of steps, and the critical section is the one at which the diagram changes sign.

The other conditions do not locate the maximum moment. Reaction = 0 would describe an unsupported point and has no general connection to where M peaks. Load = 0 is true along most of a beam that carries only point loads, so it cannot single out one section. Deflection = 0 occurs at the supports of a simply supported beam, but the maximum bending moment generally lies somewhere in the span, not at a support — so zero deflection does not mark the maximum moment. Hence the only correct criterion is shear force = 0.