Qhov kev hloov pauv siab tshaj plaws yog dab tsi?

2024 Tus sau: Miles Stephen | [email protected]. Kawg hloov kho: 2023-12-15 23:36

Rov qab los ntawm The Qhov siab tshaj plaws ntawm kev hloov pauv ntawm qhov taw tes ntawm Kev Ua Haujlwm ntawm ntau nplooj ntawv sib txawv uas yog z = f (x, y) yog ob qhov sib txawv ntawm qhov muaj nuj nqis tiag tiag thiab yog ib chav vector ces qhov qhov siab tshaj plaws ntawm kev hloov ntawm ib qho taw tes $(x, y) hauv D(f)$ yog qhov loj ntawm qhov gradient ntawm, $| abla f(x, y) |$, thiab qhov tsawg kawg nkaus tus nqi ntawm

Piv txwv li, qhov kev hloov ntawm gradient yog dab tsi?

Cov Nqi Hloov . Cov gradient ntawm kab sawv cev rau tus nqi hloov . Cov mis yog li ntawd hloov nyob rau hauv lub y axis muab faib los ntawm cov hloov hauv x axis. Hauv qhov piv txwv no uas sib npaug 10 ÷ 40 = 0.25. Qhov no sawv cev rau tus nqi ntawm 25p ib feeb thiab qhia txog qhov sib npaug tas li.

Ib yam li ntawd, dab tsi yog qhov siab tshaj qhov taw qhia derivative? Muab qhov ua haujlwm f ntawm ob lossis peb qhov sib txawv thiab taw tes x (hauv ob lossis peb qhov ntev), qhov siab kawg tus nqi ntawm cov kev taw qhia derivative thaum ntawd, Duf(x), yog |Vf(x)| thiab nws tshwm sim thaum koj muaj tib cov kev taw qhia raws li gradient vector Vf(x).

Yog li ntawd, ua li cas koj thiaj paub tias txoj kev twg yog qhov chaw siab tshaj?

2x, 2y=2?x,y; Qhov no yog vector parallel rau vector ?x, y?, yog li cov kev taw qhia ntawm steepest ascent yog ncaj qha deb ntawm lub hauv paus chiv keeb, pib ntawm qhov taw tes (x, y). Cov kev taw qhia ntawm qhov siab tshaj plaws yog li ncaj qha mus rau lub hauv paus chiv keeb los ntawm (x, y).

Nyob rau hauv dab tsi kev taw qhia yog f nce sai tshaj plaws?

Gradient yog kev taw qhia ntawm kev ua haujlwm nce ceev tshaj plaws ntawm qhov taw tes.