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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 (−1;12) where the derivative     of the function y = f(x) is equal to zero ?

$$ \\ $$$$\:\:\:{What}\:{is}\:{the}\:{number}\:{of}\:{points}\:{in}\:{the}\: \\ $$$$\:\:\:{interval}\:\left(−\mathrm{1};\mathrm{12}\right)\:{where}\:{the}\:{derivative} \\ $$$$\:\:\:{of}\:{the}\:{function}\:{y}\:=\:{f}\left({x}\right)\:{is}\:{equal}\:{to}\:{zero}\:? \\ $$

Commented by issac last updated on 29/Nov/24

Seven.  because   lim_(𝚫t→0)  ((y(t+𝚫t)−y(t))/(𝚫t))=0 (differantial coefficient)  = ((dy(t))/dt)∣_(t=α_j ) =0  α_j =0,1,3,7,9,10,11

$$\mathrm{Seven}. \\ $$$$\mathrm{because}\: \\ $$$$\underset{\boldsymbol{\Delta}{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{y}\left({t}+\boldsymbol{\Delta}{t}\right)−{y}\left({t}\right)}{\boldsymbol{\Delta}{t}}=\mathrm{0}\:\left(\mathrm{differantial}\:\mathrm{coefficient}\right) \\ $$$$=\:\frac{\mathrm{d}{y}\left({t}\right)}{\mathrm{d}{t}}\mid_{{t}=\alpha_{{j}} } =\mathrm{0} \\ $$$$\alpha_{{j}} =\mathrm{0},\mathrm{1},\mathrm{3},\mathrm{7},\mathrm{9},\mathrm{10},\mathrm{11} \\ $$

Commented by Ismoiljon_008 last updated on 30/Nov/24

   Thank you very much

$$\:\:\:{Thank}\:{you}\:{very}\:{much} \\ $$

Commented by issac last updated on 30/Nov/24

you are welcome :>

$$\mathrm{you}\:\mathrm{are}\:\mathrm{welcome}\::> \\ $$

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