Past exam of the mathematics course of the University of Cambridge 2010 iii Paper 68 4 a ii Solution Created 2026-10-03 Updated 2026-10-14
Let at an inflection point supplied by the preceding identity. Its imaginary part, divided by nonzero , gives . Its real part isAdding times the zero integral replaces by :Therefore the integrand's profile factor must be strictly negative somewhere in the open channel:This is the Fjørtoft theorem. The positive weight and the strictly negative integral establish the strict inequality, not merely a nonpositive value. It is a stronger necessary condition than Rayleigh's inflection-point theorem, and neither condition alone proves instability.