Nyob rau hauv dab tsi kev taw qhia yog qhov siab tshaj plaws ntawm kev nce?
Nyob rau hauv dab tsi kev taw qhia yog qhov siab tshaj plaws ntawm kev nce?

Video: Nyob rau hauv dab tsi kev taw qhia yog qhov siab tshaj plaws ntawm kev nce?

Video: Nyob rau hauv dab tsi kev taw qhia yog qhov siab tshaj plaws ntawm kev nce?
Video: Yuav tawm ntawm txoj kev txom nyem tau li cas? 2024, Kaum ib hlis
Anonim

Cov qhov siab tshaj plaws ntawm kev hloov yog li ntawd thiab tshwm sim nyob rau hauv lub kev taw qhia ntawm gradient, $ abla f(2, 0) = (0, 2)$, thiab qhov tsawg kawg nkaus tus nqi hloov yog thiab tshwm sim hauv lub kev taw qhia rov qab ntawm qhov gradient, uas yog $- abla f(2, 0) = (0, -2)$. Yog li ntawd.

Ib yam li ntawd, ib tug yuav nug, nyob rau hauv cov kev taw qhia twg muaj nuj nqi nce sai tshaj plaws?

Gradient yog kev taw qhia ntawm muaj nuj nqi nce sai tshaj plaws ntawm qhov taw tes. Qhov tsis zoo gradient tus nqi yog qhov kev taw qhia ntawm muaj nuj nqi txo ceev tshaj plaws ntawm qhov taw tes.

Tsis tas li ntawd, vim li cas qhov gradient taw tes rau qhov kev taw qhia ntawm kev nce siab tshaj plaws? Cov gradient ntawm ib tug multi-variable muaj nuj nqi muaj ib feem rau txhua kev taw qhia . Thiab ib yam li cov derivative tsis tu ncua, lub gradient cov ntsiab lus nyob rau hauv cov kev taw qhia ntawm loj tshaj plaws nce (ntawm no yog vim li cas: peb pauv cov lus tsa suab hauv txhua qhov kev taw qhia txaus kom them nyiaj ntau tshaj).

Tsuas yog 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).

Maximum directional derivative yog dab tsi?

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).

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