Tus txheeb ze extrema tuaj yeem tseem muaj tshwm sim ntawm qhov kawg ntawm tus sau. Piv txwv li, kev ua haujlwm f(x)=x ntawm lub sijhawm [0, 1] muaj qhov txheeb ze tshaj plaws ntawm x=1 thiab tus txheeb ze yam tsawg kawg nkaus ntawm x=0.
Puas kawg yog qhov kawg?
Tsis muaj laj thawj xav tias qhov kawg ntawm lub sijhawm yuav yog cov ntsiab lus tseem ceeb ntawm txhua yam. Yog li ntawd, peb tsis pub cov txheeb ze extrema muaj nyob rau ntawm qhov kawg ntawm lub sijhawm.
Puas muaj xwm txheej hauv zos tshwm sim ntawm qhov kawg?
Thaum f tau txhais ntawm lub sijhawm kaw, tsis muaj lub sijhawm qhib uas muaj qhov kawg ntawm lub sijhawm kaw uas f tau txhais. Li no, ib qho txiaj ntsig hauv cheeb tsam tsis tuaj yeem tshwm sim ntawm qhov kawg ntawm lub sijhawm ntawm kev sau npe.
Cov ntsiab lus kawg puas yog max lossis min?
Cov lus teb tom qab muaj qhov taw tes (1, 1), uas yog qhov kawg. Raws li cov lus txhais hauv phau ntawv kawm, kuv xav tias qhov kawg tsis tuaj yeem yog qhov tsawg kawg nkaus hauv zos lossis qhov siab tshaj plaws muabtias lawv tsis tuaj yeem nyob rau lub sijhawm qhib uas muaj lawv tus kheej. (piv txwv li: lub sijhawm qhib (1, 3) tsis muaj 1).
Yuav ua li cas paub yog tias muaj tus txheeb ze extrema?
Kev piav qhia: Rau ib qho kev ua haujlwm, txheeb ze extrema, lossis hauv zos maxima thiab minima, tuaj yeem txiav txim siab los ntawm siv thawj qhov kev xeem derivative, uas tso cai rau koj kuaj xyuas qhov kev hloov pauv ntawm f′ ib ncig ntawm lub luag haujlwm cov ntsiab lus tseem ceeb.
