Geodesic
Derivative and monotonicity
Matematičeskoe obrazovanie, Tome 104 (2022) no. 4, pp. 16-25

Voir la notice de l'article provenant de 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_104_4_a2,
     author = {M. A. Gorelov},
     title = {Derivative and monotonicity},
     journal = {Matemati\v{c}eskoe obrazovanie},
     pages = {16--25},
     publisher = {mathdoc},
     volume = {104},
     number = {4},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MO_2022_104_4_a2/}
}
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M. A. Gorelov. Derivative and monotonicity. Matematičeskoe obrazovanie, Tome 104 (2022) no. 4, pp. 16-25. http://geodesic.mathdoc.fr/item/MO_2022_104_4_a2/