Question

设x属于R+,求f(x)=x2-x+1/X的最小值

Answer 1

x^2-x+1/x=x^2-2x+1+x+1/x-1=(x-1)^2+x+1/x-1

由x+1/x≥2√(x*(1/x))=2,(x-1)^2≥0,

故得x^2-x+1/x≥0+2-1=1,

当x=1时,x^2-x+1/x=1,故f(x)=x2-x+1/X的最小值为1.