Uyifumana njani i-Extrema yeNgingqi ngoVavanyo lokuQala oluPhuma

Zonke iimalumums zengingqi kunye nobuncinci kwigrafu yomsebenzi-ebizwa ngokuba yi-extrema yendawo-yenzeka kwiindawo ezibaluleke kakhulu zomsebenzi (apho isiphumo esivela ku-zero okanye esingachazwanga). (Ungalibali, nangona kunjalo, ukuba ayizizo zonke iindawo ezibaluleke kakhulu eziyimfuneko yendawo.)

Inyathelo lokuqala lokufumana umsebenzi we-extrema yengingqi kukufumana amanani ayo abalulekileyo ( x Iimpawu zexabiso). Usebenzisa uVavanyo lokuQala oluQhelekileyo. Olu vavanyo lusekwe kwizimvo zeNobel zokufumana umvuzo njengoko uwela ngaphezulu kwenduli, kuqala uyenyuka emva koko uye ezantsi, kwaye xa uqhuba ungena uphuma entlanjeni, uyehla emva koko phezulu. Le nto yokubala iyamangalisa, eh?

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Lo mzobo ubonisa igrafu ka

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Ukufumana amanani abalulekileyo alo msebenzi, nantsi into oyenzayo.

  1. Fumana isiphumo sokuqala se f usebenzisa umgaqo wamandla.

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    iqhuma esidleleni ngakumhlathi
  2. Cwangcisa isiphumo esilingana no-zero kwaye usombulule x.

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    x = 0, -2, okanye 2.

    Ezi zintathu x- amaxabiso ngamanani abalulekileyo f. Amanani abalulekileyo ongezelelweyo anokubakho ukuba isiphumo sokuqala besingachazwanga kwezinye x -Ixabiso, kodwa ngenxa yokuba ivela

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    ichaziwe kuwo onke amaxabiso egalelo, isisombululo esisetiweyo ngasentla, 0, -2, kunye no-2, luluhlu olupheleleyo lwamanani abalulekileyo. Kungenxa yokuba isiphumo (kunye nethambeka) le f ilingana no-zero kula manani mathathu abalulekileyo, ijika linee-tangents ezithe tyaba kula manani.

Ngoku ukuba ufumene uluhlu lwamanani abalulekileyo, kuya kufuneka ujonge ukuba iincopho okanye iintlambo okanye azenzeki kwezo x -ixabiso. Unokwenza oku ngoVavanyo lokuQala oluQhelekileyo. Nantsi indlela:

  1. Thatha umgca manani uze ubeke phantsi amanani abalulekileyo owafumeneyo: 0, -2, no-2.

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    Ukwahlula lo mgca manani kwimimandla emine: ekhohlo ku-2, ukusuka -2 ukuya ku-0, ukusuka ku-0 ukuya ku-2, nasekunene kuka-2.

    amayeza okusilela kwentliziyo
  2. Khetha ixabiso kwingingqi nganye, uyixhome kwindawo yokuqala, kwaye uqaphele ukuba iziphumo zakho zilungile okanye azilunganga.

    Kulo mzekelo, ungasebenzisa amanani -3, -1, 1, no-3 ukuvavanya imimandla.

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    Ezi ziphumo zine, ngokulandelanayo, zilungile, zibi, zibi, kwaye zilungile.

  3. Thatha inombolo yakho yamanani, phawula ummandla ngamnye ngophawu olufanelekileyo oluchazayo okanye olubi, kwaye ubonise apho umsebenzi unyuka khona kwaye uncipha.

    Iyakhula apho i-derivative ilungile, kwaye iyancipha apho isiphumo singekhoyo. Theresult yinto ebizwa ngokuba yigrafu yophawu lomsebenzi.

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    Eli nani likuxelela nje oko sele ukwazi ukuba ujonge igrafu ka f -Ukuba umsebenzi unyuka kude kube ngu-2, wehle ukusuka ku-2 ukuya ku-0, ukuhla ushiye ku-0 uye ku-2, uphinde unyuke kwakhona ukusuka ku-2 kuye phambili.

    Ngoku, nantsi inzululwazi yerokethi. Umsebenzi utshintsha ukusuka ekukhuleni kuye ekunciphiseni ngo - 2; ngamanye amagama, unyuka uye ku -2 kwaye emva koko wehle. Ke, ngo-2, unayo induli okanye ubuninzi bengingqi. Kwelinye icala, ngenxa yokuba umsebenzi utshintsha ukusuka ekunciphiseni uye kunyuka ngo-2, unentlambo apho okanye ubuncinci bendawo. Kwaye ngenxa yokuba uphawu lwento yokuqala ayitshintshi kwi-zero, akukho min okanye max kuyo x -xabiso.

    yintoni i-percocet engenayo mg
  4. Fumana amaxabiso okusebenza (ngamanye amagama, ukuphakama) kwezi ndawo zimbini ze-extrema ngokufaka i x- values ​​Kumsebenzi wokuqala.

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    Ke, i-max yendawo ibekwe ku (-2, 64), kwaye imin yendawo ingo (2, -64). Ugqibile.

Sebenzisa uVavanyo lokuQala oluQalayo ukuvavanya i-extremum yendawo kwinani elithile elibalulekileyo, umsebenzi kufuneka ube gqolo ngeloxesha x- ixabiso.