Ukwedlula umsebenzi - ngolimi olulula mayelana nokuyinkimbinkimbi

Ukuze uqonde ukuthi yiziphi amaphuzu aqondile omsebenzi, akudingekile ukwazi ngokutholakala kokutholakala kokuqala nesesibili nokuqonda incazelo yawo engokwenyama. Okokuqala, udinga ukuqonda okulandelayo:

• Ama-Extremums of the work maximize noma, ngokuphambene, ukunciphisa inani lomsebenzi endaweni encane encane;
• Emkhawulweni we-extremum akufanele kube khona ukuyeka ukusebenza.

Futhi manje okufanayo, kuphela ngolimi olulula. Bheka intambo yenduku yepeni lokubhala. Uma isibambo sibheke ngokuqondile, ukubhala kuphelile, khona-ke phakathi kwebhola kuyoba yinkinga - iphuzu eliphakeme kakhulu. Kulokhu sikhuluma ngokuphezulu. Manje, uma uphendulela ipeni ngokubhala ngokuphela, kuzobe sekukhona ubuncane bomsebenzi phakathi kwebhola. Ukusebenzisa isibalo esinikezwe lapha, ungathumela ama-manipulations afakwe ohlwini lwepensela yokubhala. Ngakho-ke, ukugqithisa komsebenzi kuhlale kunamaphuzu abalulekile: maxima yayo noma minima. Isigaba esiseduze sesigrafu singaba siphumelele noma siphumelele, kodwa kufanele sibe khona ezinhlangothini zombili, kuphela kuleli cala iphuzu liyi-extremum. Uma igrafu ikhona kuphela ohlangothini olulodwa, lesi siphetho ngeke sibonakale ngisho noma izimo ezingapheli ziyaneliseka ngakolunye uhlangothi lwazo. Manje sizofunda izingxenyana zomsebenzi kusukela ekubukeni kwesayensi. Ukuze iphuzu libhekwe njengeqile, kuyadingeka futhi lanele ukuthi:

• I-derivative yokuqala ilinganiselwe i-zero noma ayikho khona ngaleso sikhathi;
• I-derivative yokuqala ishintshe uphawu lwayo kuleli phuzu.

Lesi simo siphathwa ngendlela ehlukile kusukela ekubukeni kwezinto ezivela e-oda eziphezulu: ngoba umsebenzi ohluke kakhulu endaweni okwanele ukuthi kukhona okutholakala okungaqondakali-oda okungafanani ne-zero, uma nje wonke ama-derivative we-oda elingaphansi kufanele abe khona futhi abe khona. Lona incazelo elula yama-theorems ezivela ezincwadini zamathematika aphezulu. Kodwa kubantu abavamile kakhulu kufanelekile ukuchaza leli phuzu ngesibonelo. Isisekelo siyisimo esijwayelekile. Yenza ngokushesha ukubhuka, endaweni ye-zero, inenani elincane. Izibalo ezincane kakhulu:

• Isiqalo sokuqala (X ² ) ^| = 2X, iphuzu le-zero 2X = 0;
• Isiqephu sesibili (2X) ^| = 2, ngoba iphuzu lezero z = 2.

Ngale ndlela elula, izimo ezithatha i-extrema yomsebenzi kokubili okutholakala kwe-oda zokuqala kanye nezidakamizwa ezisezingeni eliphakeme zifanekiselwa. Kungangeniswa kulokhu okuvela kokubili okukhiphayo okukodwa okungaqondakali, okungafani nalesi, okukhulunywe ngenhla. Uma kuziwa ezingxenyeni zomsebenzi eziguquguqukayo ezimbili, izimo kufanele zaneliswe ngazo zombili izimpikiswano. Uma ukukhiqizwa kokusebenza kwenzeka, khona-ke izisetshenziswa eziyimfihlo zisetshenzisiwe. Okokuthi, kuyadingeka ukuthi ube ne-extremum endaweni, ngakho-ke kokubili okutholakala kwe-oda lokuqala kulingana no-zero, noma okungenani enye yawo ayikho. Ukuze kube nokwanele kokuba khona kwe-extremum, inkulumo ibhekwa ukuthi yilokho umehluko womkhiqizo we-derivatives yesibili-oda kanye nesigcawu somkhiqizo we-second-order ohlangene womsebenzi. Uma le nkulumo ingaphezu kwezinga, khona-ke i-extremum yenzeke, futhi uma kukhona ukulingana ku-zero, umbuzo uhlala uvulekile, futhi ucwaningo olwengeziwe luyadingeka.