Calculus. Derivatives tuaj yeem pab tau! Lub derivative ntawm ib txoj haujlwm muab txoj kab nqes. Thaum txoj kab nqes nce ntxiv, txoj haujlwm yog concave upward. Thaum txoj kab nqes qis zuj zus, txoj haujlwm yog concave downward.
Yuav ua li cas yog concave thiab concave?
Concavity cuam tshuam rau tus nqi ntawm kev hloov pauv ntawm kev ua haujlwm qhov kev sib txuas. Ib txoj haujlwm f yog concave up (los yog nce) qhov twg cov derivative f′ nce. … Ib yam li ntawd, f yog concave down (los yog downwards) qhov twg tus derivative f′ yog txo (los yog sib npaug, f′f, pib superscript, prime, prime, end superscript yog tsis zoo).
Koj paub li cas yog tias lub luag haujlwm yog concave nce lossis nqis?
Yog f "(x)=0, daim duab yuav muaj qhov taw tes ntawm qhov cuam tshuam ntawm tus nqi ntawm x. Txhawm rau txheeb xyuas, xav txog tus nqi ntawm f "(x) ntawm tus nqi ntawm x rau ob sab ntawm qhov taw tes ntawm kev txaus siab. Yog tias f "(x) < 0, daim duab yog concave downward ntawm tus nqi ntawm x.
Yuav ua li cas thiaj pom qhov sib sib zog nqus?
Yuav kom nrhiav tau qhov concavity nws hloov los ntawm thiab mus rau, koj plug nyob rau hauv cov zauv ntawm ob sab ntawm inflection point. Yog tias qhov tshwm sim tsis zoo, daim duab yog concave thiab yog tias nws yog qhov zoo, daim duab yog concave.
nce thiab concave down txhais li cas?
Yog tias muaj nuj nqi nce ntxiv thiab ua kom qis, ces nws tus nqi nce qeeb; nws yog "leveling tawm." Yog hais tias qhov kev ua haujlwm yog txo qis thiab concave down, ces tus nqi ntawm kev txo qis yog txo. Kev ua haujlwm tau txo qis ntawm tus nqi nrawm dua thiab nrawm dua.
