|x|≤1,|y|≤1,求|x+y|+|y+1|+|2y-x-4|的最大值与最小值的和

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|x|≤1,|y|≤1,求|x+y|+|y+1|+|2y-x-4|的最大值与最小值的和|x|≤1,|y|≤1,求|x+y|+|y+1|+|2y-x-4|的最大值与最小值的和|x|≤1,|y|≤1,求|

|x|≤1,|y|≤1,求|x+y|+|y+1|+|2y-x-4|的最大值与最小值的和
|x|≤1,|y|≤1,求|x+y|+|y+1|+|2y-x-4|的最大值与最小值的和

|x|≤1,|y|≤1,求|x+y|+|y+1|+|2y-x-4|的最大值与最小值的和
∵|y|≤1
∴-1 ≤ y ≤1
∴ y +1≥0,
∴ |y+1| = y +1
|2y-x| ≤ |2y|+|x| ≤ 2 +1 =3
∴2y-x-4 <0
∴|2y-x-4| = -(2y-x-4)
(1)若x+y≥0,则
m =|x+y|+|y+1|+|2y-x-4|
= (x+y) +(y+1)-(2y-x-4)
= 2x +5
∵-1≤x≤1
∴3≤m≤7.
(2)若x+y<0,则
m = -(x+y) +(y+1) -(2y-x-4)
= -2y +5
∵-1 ≤ y ≤1
∴3 ≤ m ≤ 7,
综上得3≤ m ≤7.
m的最大值是7,(x = 1,y = -1时)
最小值是3.(x = -1,y = 1时)