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函数的单调性是函数的重要性质之一,有时对于一些函数的单调性我们不易做出判断时,可以使用导数进行判断:即设函数y=f(x) 在某个区间内可导,若f′(x)>0,则在这个区间上为增函数,如果f′(x)<0,则在这个区间上为减函数．但是应用时应注意在区间内 f′(x)>0是y=f(x)在此区间上为增函数的充分条件而不是必要条件．同时f′(x)<0也是在区间上为减函数的充分条件而不是必要条件．
The monotonicity of a function is one of the important properties of the function. Sometimes when we cannot easily judge the monotonicity of some functions, we can use the derivative to judge: that is, the function y=f(x) can be conducted in a certain interval, if f′(x)>0 is an increasing function in this interval. If f′(x)<0, it is a decreasing function in this interval. However, it should be noted that in the interval f′(x)>0 is y=f(x). In this interval, it is a sufficient condition but not a necessary condition to increase the function. At the same time f′(x)<0 is also a sufficient condition for decreasing the function in the interval rather than a necessary condition.