若fx=x+1/(x-2),当x为何值时fx取最小值是多少

Question

若fx=x+1/(x-2),当x为何值时fx取最小值是多少

Answer 1

f(x)=x+1/(x-2),若函数能取最小值需定义域为{x|x>2}f(x)=(x-2)+1/(x-2)+2∵x>2∴x-2>0,1/(x-2)>0根据均值定理：（x-2)+1/(x-2)≥2√[(x-2)*1/(x-2)]=2当且仅当x-2=1/(x-2),x=3时取等号∴(x-2)+1/(x-2)+2≥4即当x=3时...