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4.(06浙江卷)對a,bR,記max{a,b}=,函數(shù)f(x)=max{|x+1|,|x-2|}(xR)的最小值是____.
解:當x<-1時,|x+1|=-x-1,|x-2|=2-x,因為(-x-1)-(2-x)=-3<0,所以2-x>-x-1;當-1£x<0.5時,|x+1|=x+1,|x-2|=2-x,因為(x+1)-(2-x)=2x-1<0,x+1<2-x;當0.5£x<2時,x+1³2-x;當x³2時,|x+1|=x+1,|x-2|=x-2,顯然x+1>x-2;
故據(jù)此求得最小值為。選C