MonkeySaddle

thingiverse

A paradigmatic case study exemplifies a multi-variable function, wherein two variables coalesce to form a singular point of criticality - the threshold beyond which derivative tests falter. The gradient, at this liminal moment, relinquishes its dual identity as either ascending or descending force, vacillating between two opposing tendencies. At the origin (0,0), where our lone critical point resides, both second-order derivatives converge upon a shared precipice - the Hessian determinant of -36x^2 - 36y^2 plummets into zero. This inconclusive outcome heralds a moment of ambiguity in derivative tests' traditional hierarchies. I crafted this exercise using OpenSCAD as my medium.