Question Number 196710 by tri26112004 last updated on 30/Aug/23
$${Give}\:{the}\:{function}: \\ $$$${f}\left({x}\right)=\left({x}−\mathrm{1}\right)\left({x}−\mathrm{2}\right)^{\mathrm{2}} \left({x}−\mathrm{3}\right)^{\mathrm{3}} \left({x}−\mathrm{4}\right)^{\mathrm{4}} ...\left({x}−\mathrm{2022}\right)^{\mathrm{2022}} \\ $$$${Find}\:{extremes}\:{of}\:{f}\left({x}\right)¿ \\ $$
Commented by mr W last updated on 30/Aug/23
$${i}\:{don}'{t}\:{think}\:{they}\:{can}\:{be}\:{exactly}\: \\ $$$${determined},\:{because}\:{we}\:{can}'{t}\:{exactly} \\ $$$${solve}\:{the}\:{equation}\:{f}'\left({x}\right)=\mathrm{0},\:{i}.{e}. \\ $$$$\mathrm{ln}\:\mid{x}−\mathrm{1}\mid+\mathrm{2ln}\:\mid{x}−\mathrm{2}\mid+\mathrm{3ln}\:\mid{x}−\mathrm{3}\mid+...+\mathrm{2022ln}\:\mid{x}−\mathrm{2022}\mid=\mathrm{0}. \\ $$