已知A为大于0的常数,求函数F(X)=(AX^2+X+1)/(X+1)(X>=3)的最小值_数学解答

已知A为大于0的常数,求函数F(X)=(AX^2+X+1)/(X+1)(X>=3)的最小值

人气：329 ℃　时间：2019-08-21 12:56:41

解答

F(X)=(X+1)/(X+1)+(AX^2+AX-AX)/(X+1)
=1+AX(X+1)/(X+1)+(-AX)/(X+1)
=1+AX+(-AX-A+A)/(X+1)
=1+AX-A(X+1)/(X+1)+A/(X+1)
=1+AX-A+A/(X+1)
=1+AX+A-2A+A/(X+1)
=1-2A+A(X+1)+A/(X+1)
>=1-2A+A√2