已知x大于0,Y大于0,XY等于8,则X加2y的最小值是如题

已知x大于0,Y大于0,XY等于8,则X加2y的最小值是如题
已知x大于0,Y大于0,XY等于8,则X加2y的最小值是如题

已知x大于0,Y大于0,XY等于8,则X加2y的最小值是如题
已知x大于0,Y大于0,XY等于8,所以：f(x,y) = x + 2y = x + 2*8/x = x + 16/x df(x,y)/dx = 1 - 16/(x^2)==> 当df(x,y)/dx = 1 - 16/(x^2) =0,即x=4时,f(x,y)有极值8.因为,x等于5时,f(5,8/5) = 5 + 16/5 > 8; x等于3时,f(3,8/3) = 3 + 16/3 > 8.所以,x + 2y有极小值8.