Let p(m)(x) = P-m((lambda))(x)/P-m((lambda))(1) he the m-th ultraspherical pohnomial noronalioed by p(m)(1) = 1. We prove the inequality vertical bar x vertical bar p(n)(2)(x)-p(n-1)(x)p(n+1)(x) >= 0, x is an element of [-1,1] for 1/2 < lambda <= 1/2. Equality holds only for x = +/- 1 and, if a is even, for x = 0. Further partial results on an extension of this inequality to normalized Jacobi polynomials are given.