Yuav kom nrhiav tau thaum muaj nuj nqi yog concave, koj yuav tsum xub coj 2nd derivative 2nd derivative Qhov thib ob derivative ntawm ib tug muaj nuj nqi f siv tau los txiav txim qhov concavity ntawm daim duab f. Ib qho kev ua haujlwm uas nws qhov thib ob yog qhov zoo yuav ua rau concave (tseem hu ua convex), txhais tau hais tias cov kab tangent yuav pw hauv qab daim duab ntawm txoj haujlwm. https://en.wikipedia.org › wiki › Second_derivative
Second derivative - Wikipedia
tom qab ntawd muab nws sib npaug rau 0, thiab tom qab ntawd nrhiav ntawm qhov twg xoom qhov txiaj ntsig qhov kev ua haujlwm tsis zoo. Tam sim no sim ntsuas qhov tseem ceeb ntawm txhua sab ntawm cov no kom pom thaum lub luag haujlwm tsis zoo, thiab yog li txo qis.
Koj pom qhov concavity ntawm daim duab li cas?
Peb tuaj yeem xam qhov thib ob derivative los txiav txim qhov concavity ntawm txoj haujlwm nkhaus ntawm txhua qhov taw tes
- Xau qhov thib ob derivative.
- Hloov tus nqi ntawm x.
- Yog f "(x) > 0, daim duab yog concave upward ntawm tus nqi ntawm x.
- Yog f "(x)=0, daim duab yuav muaj qhov taw tes ntawm kev cuam tshuam ntawm tus nqi ntawm x.
Koj pom qhov ua haujlwm concave li cas?
Yuav kom paub tias nws yog concave los yog convex, saib qhov thib ob derivative. Yog tias qhov tshwm sim zoo, nws yog convex. Yog hais tias tsis zoo, ces nws yog concave. Txhawm rau nrhiav qhov thib ob derivative, peb rov ua cov txheej txheem siv raws li peb cov lus qhia.
Yuav ua li cas thiaj nrhiav tau txoj kab sib dhos?
Peb tuaj yeem nrhiav tauconcavity ntawm ib tug muaj nuj nqi los ntawm nrhiav nws ob derivative (f''(x)) thiab qhov twg nws yog sib npaug rau xoom. Cia peb ua li ntawd! Yog li qhov no qhia peb tias cov haujlwm linear yuav tsum nkhaus ntawm txhua qhov chaw. Paub tias daim duab ntawm kev ua haujlwm yog ib txoj kab ncaj nraim, qhov no tsis tsim nyog, puas yog?
Yuav ua li cas koj thiaj pom qhov tsis sib haum xeeb?
Yuav Ua Li Cas Pom Qhov Nruab Nrab ntawm Concavity thiab Inflection Points
- Nrhiav qhov thib ob derivative ntawm f.
- Teem thib ob derivative sib npaug rau xoom thiab daws.
- Txiav txim siab seb qhov thib ob derivative tsis tau txhais rau ib qho x-tus nqi. …
- Tshaj cov lej no ntawm ib kab ntawm tus lej thiab sim cov cheeb tsam nrog tus lej thib ob.
