求函数单调区间的步骤

导函数的本质就是原函数各处的斜率所表现出的变化规律，用函数表示，就是导函数了。

若让导函数>0，求出的就是斜率大于0的x的范围，就是单调增的区间，令导函数=0，就是看原函数的拐点，极致，也是函数单调性发生改变的临界的x值。

求该函数的导函数，让该导函数大于0，就出的区间就是增区间，小于0求出的区间就是减区间。

（注意原函数的定义域） 第二种方法就是定义法。

扩展资料：若函数y=f(x)在某个区间是增函数或减函数，则就说函数在这一区间具有（严格的）单调性，这一区间叫做函数的单调区间。

此时也说函数是这一区间上的单调函数。

注：在单调性中有如下性质。

图例：↑（增函数）↓（减函数）↑+↑=↑ 两个增函数之和仍为增函数↑-↓=↑ 增函数减去减函数为增函数↓+↓=↓ 两个减函数之和仍为减函数↓-↑=↓ 减函数减去增函数为减函数参考资料来源：百度百科-单调区间已赞过已踩过已赞过已踩过已赞过已踩过<你对这个回答的评价是？评论收起 ._4m59a3r{padding:30px 0 20px 42px;border:0;background-color:#fff;position:relative;zoom:1;margin-bottom:10px}._4m59a3r.ec-1841{padding:20px 0}._4m59a3r.ec-2246{padding:20px 0 10px}.ec-1841 ._44pkrw8{font-size:16px;margin-bottom:-5px}._44pkrw8{position:relative;overflow:hidden;line-height:25px;height:25px;color:#7a8f9a}._44pkrw8 h2{margin:0;padding:0}._44pkrw8:after{content:" ";display:block;height:0;clear:both;visibility:hidden}a._53wjrpp{float:right;color:#666;text-decoration:none;font-size:12px;margin-left:8px}._3sjgky6{font-size:13px;line-height:normal;color:#666;line-height:20px;margin-top:10px}._5qv9qjj{position:relative;margin-top:15px}._5qv9qjj h3{padding:0;font-weight:400}._5qv9qjj a{text-decoration:none}._5qv9qjj em{color:#d81419;font-style:normal}.ec-2246 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（注意原函数的定义域）第二种方法就是定义法。

利用导数求解多项式函数单调性的一般步骤：①确定f（x）的定义域；②计算导数f′（x）；③求出f′（x）=0的根；④用f′（x）=0的根将f（x）的定义域分成若干个区间，列表考察这若干个区间内f′（x）的符号，进而确定f（x）的单调区间：f′（x）>0，则f（x）在对应区间上是增函数，对应区间为增区间；f′（x）<0，则f（x）在对应区间上是减函数，对应区间为减区间。

含义对于可导的函数f(x)，x↦f'(x)也是一个函数，称作f(x)的导函数（简称导数）。

寻找已知的函数在某点的导数或其导函数的过程称为求导。

实质上，求导就是一个求极限的过程，导数的四则运算法则也来源于极限的四则运算法则。

反之，已知导函数也可以反过来求原来的函数，即不定积分。

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