求/x-1/+/x+2/+······+/x+10/最小值

题目

求/x-1/+/x+2/+······+/x+10/最小值

答案

根据/x+1/+/x+2/+······+/x+10/的图形,可得出最小值在[-10,-1]内取得
当x=-10或x=-1时/x+1/+/x+2/+······+/x+10/=0+1+2+3+.+9=45
当x=-9或x=-2时/x+1/+/x+2/+······+/x+10/=1+0+1+2+3+.+8=37
当x=-8或x=-3时/x+1/+/x+2/+······+/x+10/=2+1+0+1+2+3+.+7=31
当x=-7或x=-4时/x+1/+/x+2/+······+/x+10/=3+2+1+0+1+2+3+.+6=27
当x=-6或x=-5时/x+1/+/x+2/+······+/x+10/=4+3+2+1+0+1+2+3+.+5=25
所以/x+1/+/x+2/+······+/x+10/的最小值为25,此时x=-6或x=-5.