证明f(x)=4x次方+1分之2x次方在(0,1)上是减函数?

问题描述:

证明f(x)=4x次方+1分之2x次方在(0,1)上是减函数?

f(x)=x²+2/x令0<x1<x2<1f(x1)-f(x2)=x1²+2/x1-x2²-2/x2通分=(x1³x2+2x2-x1x2³-2x1)/(x1x2)x1,x2都是正数,分母大于0分子=(x1³x2-x1x2³)+(2x2-2x1)=x1x2(x1²-x2&...