On inequalities for norms of intermediate derivatives on a finite interval - Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A. (Ukrains’kyi Matematychnyi Zhurnal, 1995)
For functionsf which have an absolute continuous (n−1)th derivative on the interval [0, 1], it is proved that, in the case ofn>4, the inequality $$\left\| {f^{(n - 2)} } \right\|_∞ \leqslant 4^{n - 2} (n - 1) ! \left\| f \right\|_∞ + \left\| {f^{(n)} } \right\|_∞ /2$$ holds with the exact constant 4 n−2(n−1)!.