Summary: Let \(f:[a,b]\to\mathbb{R}\) be a continuous function such that the \(n\)-th order symmetric Laplace derivative \(SLD^nf\) exists in \((a,b)\). It is proved that if \(SLD^nf\), \(SLD^{n-2}f\), \(SLD^{n-4}f, \ldots\) are Darboux and Baire\(^\ast1\) in \((a,b)\) and if the upper symmetric Laplace derivative \(\overline{SLD}^{n+2}f\) is non-negative in \((a,b)\), then the ordinary \(n\)-th order derivative \(f^{(n)}\) exists and is convex in \((a,b)\).