Conclusion: nyob rau 'sab nraum' ncua sij hawm (−∞, xo), muaj nuj nqi f yog concave upward yog f″(to)>0 thiab yog concave downward yog f″(to)<0. Ib yam li ntawd, ntawm (xn, ∞), txoj haujlwm f yog concave upward yog f″(tn)>0 thiab yog concave downward yog f″(tn)<0.
Qhov twg f yog concave?
Daim duab ntawm y=f (x) yog concave upward ntawm cov ntu uas y=f "(x) > 0. Daim duab ntawm y=f (x) yog concave downward ntawm cov ntu uas y=f"(x) < 0. Yog tias daim duab ntawm y=f (x) muaj qhov taw tes ntawm kev cuam tshuam ces y=f "(x)=0.
Koj pom li cas yog tias muaj nuj nqi concave nce lossis nqis?
Kev muab qhov thib ob qhia tau rau peb yog tias txoj kab nqes txuas ntxiv nce lossis txo
- Thaum qhov thib ob derivative yog qhov zoo, txoj haujlwm yog concave upward.
- Thaum qhov thib ob derivative tsis zoo, lub luag haujlwm yog concave downward.
Yuav ua li cas koj pom lub sijhawm ntawm kev sib tw?
Yuav Ua Li Cas Nrhiav 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 seb qhov thib ob derivative tsis tau txhais rau ib qho x-tus nqi. …
- Thov cov lej no rau ntawm tus lej kab thiab sim cov cheeb tsam nrog tus lej thib ob.
Yuav ua li cas sau cov lus sib dhos?
Koj ntsuas qhov tseem ceeb ntawm sab laug thiab sab xis mus rau qhov thib ob derivative tab sis tsis yog qhov tseeb ntawm x. Yog tias koj tau txais tus lej tsis zoo ces nws txhais tau hais tias ntawm lub sijhawm ntawd qhov kev ua haujlwm yog concave thiab yog tias nws zoo nws concave. Koj yuav tsum nco ntsoov tias cov ntsiab lus f(0) thiab f(3) yog cov ntsiab lus inflection.