已知函数f(x)=axˇ+2ax+4(0∠a∠3),若x1∠ x2 且x1 +x2=1-a,则判断f(x1)与f(x2)的大小关系请详解
问题描述:
已知函数f(x)=axˇ+2ax+4(0∠a∠3),若x1∠ x2 且x1 +x2=1-a,则判断f(x1)与f(x2)的大小关系请详解
答
x1+x2=1-a--->x1=1-a-x2
f(x1)-f(x2) = a(x1²-x2²)+2a(x1-x2)+(4-4)
= a(x1+x2)(x1-x2)+2a(x1-x2)
= [a(1-a)+2a](x1-x2)
= a(3-a)(x1-x2)
0<a<3--->a(3-a)>0
x1<x2 --->f(x1)<f(x2)