knrt.net
当前位置:首页 >> z x 3y 2 3xy 3 xy 1 >>

z x 3y 2 3xy 3 xy 1

z=x³+y³-3xy(x-y) ∂z/∂x=3x²-3y(x-y)-3xy=3x²-6xy+3y² ∂z/∂y=3y²-3x(x-y)+3xy=3y²+6xy-3x² ∂²z/∂x²=6x-6y ∂²z/∂x∂y=6y+6x W...

z=x^2+3xy+y^2 ∂z/∂x = 2x+3y ∂z/∂x|(1,0) = 2+0 =2 ------ ∂z/∂y = 3x +2y ∂z/∂y|(1,0) = 3 +0 =3

把式中含w的项合并,得 M=xw+2yw+3xy+3zw+4xz+5yz=(x+2y+3z)w+3xy+4xz+5yz 将w=1-x-y-z代入上式,整理得M=(x+2y+3z)-(x^2+2y^2+3z^2) =(x-x^2)+2(y-y^2)+3(z-z^) =1/4-(x-1/2)^2+2/4-2(y-1/2)^2+3/4-(z-1/2)^2 =6/4-(x-1/2)^2-2(y-1/2)^2-(z-1/...

1=(x²+4y²-3xy)/z≥(4xy-3xy)/z, 故则当xy/z取得最大值时x²=4y²,x=2y,z=x²+4y²-3xy=2y² 2/x+1/y-2/z=2/y-1/y²=1-(1/y-1)²≤1 即当y=1,x=2,z=2时取最大值1

(1)由题意可得,z=1-2x-2y,故M=3xy+yz+zx=3xy+(x+y)z=3xy+(x+y)[1-2(x+y)]=3xy+(x+y)-2(x+y)2≤3?(x+y)24+(x+y)-2(x+y)2=-54(x+y)2+(x+y),当且仅当x=y时,取等号.令t=x+y,则M≤-54t2+t=-54(t?25)2+15≤15,当且仅当t=x+y=2...

∵x 2 -3xy+4y 2 -z=0,∴z=x 2 -3xy+4y 2 ,又x,y,z均为正实数,∴ xy z = xy x 2 -3xy+ 4y 2 = 1 x y + 4y x -3 ≤ 1 2 x y × 4y x -3 =1(当且仅当x=2y时劝=”),∴ ( xy z ) max =1,此时,x=2y.∴z=x 2 -3xy+4y 2 =(2y) 2 -3×2y×y+4y 2 =2y...

z=x^2+3xy+y^2 对x求偏导数的话,y就看作常数, 那么x^2对x求偏导数得到2x, 3xy对x求偏导数得到3y 而y^2对x求偏导就是0 所以偏导数的结果为2x+3y

驻点定义

无法正常回答

网站首页 | 网站地图
All rights reserved Powered by www.knrt.net
copyright ©right 2010-2021。
内容来自网络,如有侵犯请联系客服。zhit325@qq.com