Video: Yuav ua li cas koj paub yog hais tias muaj nuj nqi yog concave?
2024 Tus sau: Miles Stephen | [email protected]. Kawg hloov kho: 2023-12-15 23:36
Yog f "(x) > 0, cov duab yog concave upward ntawm uas nqi x. Yog f "(x) = 0, lub graphmay muaj ib qho point of inflection ntawm uas nqi x. Rau kuaj , xav txog tus nqi ntawm f "(x) ntawm qhov tseem ceeb ntawm x mus rau ib sab ntawm qhov kev txaus siab. Yog f "(x) <0, cov duab concave nqes at uas nqi x.
Tsis tas li ntawd, nws txhais li cas rau kev ua haujlwm kom concave?
1. Ib qho txawv muaj nuj nqi f yog (tseem ceeb) concave ntawm ib ntus yog tias thiab tsuas yog nws qhov kev hloov pauv muaj nuj nqi f ' yog (nruj me ntsis) monotonically txo qis ntawm lub sijhawm ntawd, uas yog , a concave muaj nuj nqi ib qho tsis nce (txo) txoj kab nqes. Points qhov twg concavity kev hloov pauv (nruab nrab concave thiab convex) yog inflection cov ntsiab lus.
Ib yam li ntawd, puas muaj nuj nqi concave lossis convex? Nyob rau hauv lej, tus nqi tiag muaj nuj nqi txhais onan n-dimensional interval hu ua convex (los yog convex nqes los yog concave upward) yog cov kab ntu nruab nrab ntawm ob lub ntsiab lus ntawm daim duab ntawm tus muaj nuj nqi lus dag saum toj no los yog ntawm daim duab.
Kuj paub yog, ua li cas koj thiaj paub tias muaj nuj nqi yog convex?
Yog tias f'(x)≧0 rau tag nrho x∈(a, b), ces tus muaj nuj nqi f(x) yog convex downward (los yog concaveupward) ntawm lub caij [a, b]; Yog tias f'(x)≦0 rau allx∈(a, b), ces tus muaj nuj nqi f(x) yog convex upward (los yog concave downward) ntawm lub caij [a, b].
Puas yog concave positive lossis negative?
A concave iav qhov tsua nyob rau ntawm qhov khoom; whereas. Ib daim iav convex flexes deb ntawm qhov khoom. r. Los ntawm kev sib tham, qhov kev ncua deb yog ntsuas, raws lub hauv paus axis, xws li zoo los ntawm daim iav nyob rau hauv cov kev taw qhia ntawm cov khoom thiab tsis zoo deb ntawm qhov khoom.
Pom zoo:
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