Mathematics · Soil Mechanics

Consider a point force P acting on the surface of a homogeneous, elastic half-space (Boussinesq's problem). The vertical stress σz at any point (r, z) within the half-space is given by σz = 3P z32π (r2 + z2)5/2, where r is the radial distance and z is the depth. At any given constant radial distance r, what is the mathematical relationship defining the depth z at which the vertical stress σz reaches its maximum value?