Question Number 214152 by Ismoiljon_008 last updated on 29/Nov/24
Commented by Ismoiljon_008 last updated on 29/Nov/24
$$ \\ $$$$\:\:\:{What}\:{is}\:{the}\:{number}\:{of}\:{points}\:{in}\:{the}\: \\ $$$$\:\:\:{interval}\:\left(−\mathrm{1};\mathrm{12}\right)\:{where}\:{the}\:{derivative} \\ $$$$\:\:\:{of}\:{the}\:{function}\:{y}\:=\:{f}\left({x}\right)\:{is}\:{equal}\:{to}\:{zero}\:? \\ $$
Commented by issac last updated on 29/Nov/24
$$\mathrm{Seven}. \\ $$$$\mathrm{because}\: \\ $$$$\underset{\boldsymbol{\Delta}{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{y}\left({t}+\boldsymbol{\Delta}{t}\right)−{y}\left({t}\right)}{\boldsymbol{\Delta}{t}}=\mathrm{0}\:\left(\mathrm{differantial}\:\mathrm{coefficient}\right) \\ $$$$=\:\frac{\mathrm{d}{y}\left({t}\right)}{\mathrm{d}{t}}\mid_{{t}=\alpha_{{j}} } =\mathrm{0} \\ $$$$\alpha_{{j}} =\mathrm{0},\mathrm{1},\mathrm{3},\mathrm{7},\mathrm{9},\mathrm{10},\mathrm{11} \\ $$