已知函数f(x)=(3-x)/(4x+1),求证f(x)在（-1/4,+∞)上递减

题目

已知函数f(x)=(3-x)/(4x+1),求证f(x)在（-1/4,+∞)上递减

答案

先化为
f(x)=(3-x)/(4x+1),
=(-1/4)(x-3)/(x+0.25)
=(-1/4)[(x+0.25)-3.25]/(x+0.25)
=-1/4+3.25/(x+0.25)
再用单调函数的定义证明.