Applied Mathematics. A Journal of Chinese Universities. Ser. B (Appl. Math. J. Chinese Univ. Ser. B) (20110101), 26, no.~4, 379-389. ISSN: 1005-1031 (print).eISSN: 1993-0445.
In the paper, the authors discuss the extremum of second-order directional derivatives, i.e.\ the gradient of first-order derivatives. For given second-order directional derivatives in three nonparallel directions and for given second-order directional derivatives and mixed directional derivatives in two nonparallel directions, the authors establish formulas for the extremum of second-order directional derivatives and show that the directions corresponding to maximum and minimum are perpendicular to each other.