What is the relationship between shear force, bending moment, and loading?

The relationships are: dV/dx = -w (rate of change of shear equals negative of distributed load), dM/dx = V (rate of change of moment equals shear force). Point loads cause sudden changes in SF, and point moments cause sudden changes in BM. Maximum bending moment occurs where shear force is zero or changes sign. These relationships are fundamental for drawing SFD and BMD.