Question

已知xy∈R+,满足3x+y-xy=0,则x+3y的最小值为

Answer 1

由题意得y不等于3

若y=3,则3x+3-3x=0,这显然是不成立的,故y不等3

所以,x=y/(y-3)

A= x+3y=y/(y-3) +3y

通分得 A=(3y^2 -8y)/(y-3)=f(y)

求导:f'(y)=[3(y^2-6y+8)]/(y-3)^2

令f'(y)=0 y=2 或 y=4

y=2时,x=-2

y=4时,x=4

故(x+3y)max=4+3*4=16