解
當x≤-1時,f（x）=-15x-5,為減函數(shù),最小值為f（-1）=10
當-1≤x≤-1/2時,f（x）=-13x-3,為減函數(shù),最小值為f（-1/2）=7/2
當-1/2≤x≤-1/3時,f（x）=-9x-1,為減函數(shù),最小值為f（-1/3）=2
當-1/3≤x≤-1/4時,f（x）=-3x+1,為減函數(shù),最小值為f（-1/4）=7/4
當-1/4≤x≤-1/5時,f（x）=5x+3,為增函數(shù),最小值為f（-1/4）=7/4
當x≥-1/5時,f（x）=15x+5,為增函數(shù),最小值為f（-1/5）=2

由此可見f（x）=|x+1|+|2x+1|+|3x+1|+|4x+1|+|5x+1|的最小值是7/4