函數之單調性者，亦省作單調性，增減性，函數連續之本德也，其況有四，增減平轉是也。
例：有函數f(x)=2x−1 ,x∈[2,6]{\displaystyle f(x)={\frac {2}{x-1}}\ ,x\in [2,6]} 者，試論其增減性
解：設x1 , x2，且2⩽x1<x2⩽6{\displaystyle 2\leqslant x_{1}<x_{2}\leqslant 6} ，則
f(x2)−f(x1)=2x2−1−2x1−1{\displaystyle f(x_{2})-f(x_{1})={\frac {2}{x_{2}-1}}-{\frac {2}{x_{1}-1}}}
=2[(x1−1)−(x2−1)](x1−1)(x2−1){\displaystyle ={\frac {2[(x_{1}-1)-(x_{2}-1)]}{(x_{1}-1)(x_{2}-1)}}}
=2(x1−x2)(x1−1)(x2−1){\displaystyle ={\frac {2(x_{1}-x_{2})}{(x_{1}-1)(x_{2}-1)}}}
=−2(x2−x1)(x1−1)(x2−1){\displaystyle =-{\frac {2(x_{2}-x_{1})}{(x_{1}-1)(x_{2}-1)}}}
<0{\displaystyle <0}
故其遞減
見導數頁
![{\displaystyle f(x)={\frac {2}{x-1}}\ ,x\in [2,6]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c732a887a17f12c823c711db6b8ca1b4aad36c7b)
者，試論其增減性
，則
![{\displaystyle ={\frac {2[(x_{1}-1)-(x_{2}-1)]}{(x_{1}-1)(x_{2}-1)}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1eebf9d629f3cf4764088d253d5417d7ca823009)
