Cov txheej txheem:

Dab tsi yog qhov point of inflection hauv lej?
Dab tsi yog qhov point of inflection hauv lej?

Video: Dab tsi yog qhov point of inflection hauv lej?

Video: Dab tsi yog qhov point of inflection hauv lej?
Video: How to Find Inflection Points 2024, Kaum ib hlis
Anonim

Nyob rau hauv qhov sib txawv calculus, ib inflection point , point of inflection , flex, lub ua paug (Lus Askiv Askiv: inflexion ) yog a taw tes nyob rau hauv ib tug nruam dav hlau nkhaus ntawm qhov nkhaus hloov ntawm concave (concave downward) rau convex (concave upward), los yog vice versa.

Kuj paub, koj pom qhov point ntawm inflection li cas?

Cov ntsiab lus

  1. Ib qho taw tes inflection yog ib qho taw tes ntawm daim duab ntawm ib qho kev ua haujlwm uas qhov kev hloov pauv hloov.
  2. Cov ntsiab lus ntawm inflection tuaj yeem tshwm sim qhov twg qhov thib ob derivative yog xoom. Hauv lwm lo lus, daws f ' = 0 txhawm rau nrhiav cov ntsiab lus muaj peev xwm cuam tshuam.
  3. Txawm hais tias f '(c) = 0, koj tsis tuaj yeem xaus tias muaj kev cuam tshuam ntawm x = c.

Qhov thib ob, pes tsawg lub ntsiab lus yog inflection? Inflection point yog qhov chaw ua haujlwm hloov concavity. Qhov thib ob derivative yuav tsum sib npaug zero thaum lub luag haujlwm hloov concavity. Tab sis peb yuav tsum tau kuaj cov ntsiab lus ntawm ob sab kom paub tseeb tias qhov concavity yeej hloov. Yog li, x = 15√21 yog qhov ua tau inflection point.

Xav txog qhov no, dab tsi tsis muaj lub ntsiab lus ntawm kev cuam tshuam?

Piav: A point of inflection yog a taw tes ntawm daim duab uas qhov concavity ntawm daim duab hloov. Yog tias muaj nuj nqi tsis tau txhais ntawm qee tus nqi ntawm x, muaj ua tau ua tsis muaj inflection point . Txawm li cas los, concavity ua tau hloov thaum peb dhau mus, sab laug mus rau sab xis hla ib qho x qhov tseem ceeb uas cov haujlwm tsis tau txhais.

Puas yog cov ntsiab lus inflection yuav tsum muaj nyob hauv qhov sau npe?

Yog hais tias muaj nuj nqi hloov ntawm concave upward mus rau concave downward los yog vice versa nyob ib ncig ntawm a taw tes , npe a taw tes ntawm ua paug ntawm lub luag haujlwm. Hauv kev txiav txim siab lub sijhawm uas qhov kev ua haujlwm yog concave upward lossis concave downward, koj xub pom sau npe tus nqi qhov twg f″(x) = 0 los yog f″(x) ua tsis muaj nyob.

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