Derivative and monotonicity
Matematičeskoe obrazovanie, no. 4 (2022), pp. 16-25
Cet article a éte moissonné depuis la source Math-Net.Ru
The article presents several proofs of the growth of a function with a positive derivative, which do not use the developed apparatus of differential calculus - Fermat's, Rolle's, Lagrange's theorems. The questions of the fundamental non-elementarity of such proofs are discussed, as well as the expediency of including this topic in the school mathematics course.
@article{MO_2022_4_a2,
author = {M. A. Gorelov},
title = {Derivative and monotonicity},
journal = {Matemati\v{c}eskoe obrazovanie},
pages = {16--25},
year = {2022},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MO_2022_4_a2/}
}
M. A. Gorelov. Derivative and monotonicity. Matematičeskoe obrazovanie, no. 4 (2022), pp. 16-25. http://geodesic.mathdoc.fr/item/MO_2022_4_a2/
[1] P. S. Aleksandrov, P. S. Uryson, Memuar o kompaktnykh topologicheskikh prostranstvakh, Nauka, M., 1971, 144 pp.
[2] S. M. Nikolskii, Kurs matematicheskogo analiza. T. 1., Nauka, M., 1983, 464 pp. | MR
[3] N. Ya. Vilenkin, S. I. Shvartsburd, Matematicheskii analiz, Prosveschenie, M., 1969, 576 pp.
[4] L. S. Pontryagin, Matematicheskii analiz dlya shkolnikov, Nauka, M., 1980, 88 pp.
[5] Ya. B. Zeldovich, I. M. Yaglom, Vysshaya matematika dlya nachinayuschikh fizikov i tekhnikov, Nauka, M., 1982, 512 pp.
[6] L. S. Pontryagin, Zhizneopisanie L.S. Pontryagina, matematika, sostavlennoe im samim, IChP “Prima V”, M., 1998, 304 pp. | MR
[7] V. I. Arnold, Chto takoe matematika?, MTsNMO, M., 2002, 104 pp.