Question

已知a小b小于c小于d.求|x-a|+|x-b|+|x-c|+|x+d|的最小值

Answer 1

|x-a|+|x-b|+|x-c|+|x-d|

=(|x-a|+|x-d|)+(|x-c|+|x-b|)

≥|(x-a)-(x-d)|+||(x-b)-(x-c)|

=|d-a|+|c-b|

=d-a+c-b.