作者pp20624 (kk)
看板trans_math
标题Re: [考古] 98东华
时间Mon Jun 13 15:28:57 2011
依照上面大大给的提示
还是有些不了解
use the method of lagrange multipliers to find the point on
the unit circle closest to the point (3,4)
f(x,y)= (x-3)^2 + (y-4)^ +λ(x^2 + y^2 -1)
fx = 2(x-3)+2λx=0 6-x 4-y
fy = 2(y-4)+2λy=0 λ=------ = ------
x y
y=2/3 x
代回x^2 + y^2 =1 ,
x^2 + 4/9 x^2 =1 ,
x^2(1+4/9)=1
这边我就卡关了 可能我上面整段都弄错？？
--------------------------
find and classify the relative extrema
of f(x)=x(1-x)^1/3
f(x)=x(1-x)^1/3
=x^1/3 - x^2/3
f'(x)=1/3 x^-2/3 - 2/3 x^-1/3
=1/3 x^-1/3 (x-2)
f'(x)=0 x=2 , f'(x)不存在 x=0
f'(2+)>0 , f'(2-)< 0 极小
f'(0+)<0 , f'(0-)> 0 极大
後面就？？
有请大大指点
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※ 编辑: pp20624 来自: 210.240.175.75 (06/13 15:30)
※ 编辑: pp20624 来自: 210.240.175.75 (06/13 15:30)