函数f(x)= x + 1/x -1(x≥2),则f(x)的最小值是___________
问题描述:
函数f(x)= x + 1/x -1(x≥2),则f(x)的最小值是___________
答
f(x)=x+[1/(x-1)]=1+(x-1)+[1/(x-1)]≥1+2=3.等号仅当x=2时取得,∴f(x)min=3.
函数f(x)= x + 1/x -1(x≥2),则f(x)的最小值是___________
f(x)=x+[1/(x-1)]=1+(x-1)+[1/(x-1)]≥1+2=3.等号仅当x=2时取得,∴f(x)min=3.