Question

若x>2,求函数f(x)=(x^2+12)/(x-2)的最小值.

Answer 1

(x^2+12)/(x-2)=(x^2-4)/(x-2)+(12+4)/(x-2)=x+2+16/(x-2)=x-2+16/(x-2) +4

x-2>0

x-2+16/(x-2) +4>=2根号16+4=8+4=12

当x-2=16/(x-2) x-2=4 x=6时取最小值， f(x)min=12