KE至肆上 14

 

邢怂列肆由劣耘 LAGRANGE

 

阁豉 g 篚礤齄 溟狯锺唧殪 篚碥耵珞 赳轾 戾翎怆玺 f 篚礤齄 溟狯锺唧殪 篚碥耵珞 锺轶燧礴 篝 犴镩牯 U 麸 镳镞 疱耖蓣彘 翮 屦轹茼彘 g(X)=0. 容腼蹯 磲 怦稞戾 翎 箸戾哚 疖睐 篝珥 屦轹茼彘 g(X)=0 篝 镳镞 f 蓣彘 彡顸翎麸.

儒珈: 阁豉 S 麸 簖盹腼 豉 箸戾啭 痫 殛犴镳镩稞 g(X)=0 gradg(X)0. A 暹磲 蓓 箸戾唢 篝 镳镞 f 彡顸翎麸 S 酎翦 躔荞麇 瘃徙灬糸挈 ..

gradf(P) = gradg(P).

A豸 箸灬唔彘  汩 磲 怦稞戾 翎 彡顸翎翎 翮 f 瘃蒺彘 磲 怦稞戾  翎 箸戾哚 痫 殛犴镳镩稞 翮 疳襻疖睐 孱唧 赆 戾翎 磲 篚汴襁盹蹯 糸 糸燧 f 蟠狨糗 翎 箸戾哚. 另 躔荞麇 疱疱襻箪蓓矧 狁殍禳 箸戾啭 戾 gradg(X)=0 酎翦 篚汴襁盹蹯 糸 糸燧 f 蟠狨糗 翎 箸戾哚 戾 狨糨 痫 怦揸犰 瘃镧泔蹯蓓.

葬 疳襻疖睐 轶鼾秕 赆 汩 n 戾翎怆玺蒡.

 

馏贽箦轵

1. 躔镫镢唧弭 麸 咫荀轶麸 翮 篚碥耵珞珧 f(x,y) = xy 疖睐 篝 簖盹腼 x-y=1. [她箸]

2. 怦暹翦 糸 溟狍糗箦轵 牾腴礓耖觑 滹麇唢 戾 赆疖觊 痫 蓣彘 翮 咫荀轶翮 漉磲艮 屦轹茼彘 鼯褴彘 彡耖恂 蓓 脒赳 礤耧. [她箸]

3. 艴皴栾 翎 彡顸翎翎 翮 篚碥耵珞珧 f(x,y,z) = x2-y+z 戾 麸躜 疱耖锺轶祜 x2+y2=1/4 x-z=1. [她箸]

 

[绣耖鬻屙]