![](https://img.haomeiwen.com/i20882701/5f8024ea62b67422.png)
极限的保号性和极值的定义,也可以用特殊函数y=x²代入极值是个局部形态,只和这个点有关系,所以只要看这个点的小邻域两侧恒定大于0或小于0
![](https://img.haomeiwen.com/i20882701/6a5ec1f52bf5c19f.png)
当函数求导较为复杂的时候,换一种思路
![](https://img.haomeiwen.com/i20882701/818d3afd076cec98.png)
解法:
1.水平渐近线—x趋向于无穷,y会不会趋向有限值
不管是x趋向于负无穷,还是x趋向于正无穷,只要有一侧的极限存在趋向于有限值,这条渐近线就是存在
2.垂直渐近线—x趋向于有限值,y趋向于无穷
考虑分母为0处
3.斜渐近线—x趋向于无穷,斜率趋向于a,截距趋向于b
![](https://img.haomeiwen.com/i20882701/65120f70f97b5c8a.png)
e无穷!!错选B
![](https://img.haomeiwen.com/i20882701/d36b516faeffb897.png)
1.连续,两端点异号,连续函数零点定理
![](https://img.haomeiwen.com/i20882701/72d4910885be7a12.png)
2.罗尔定理
![](https://img.haomeiwen.com/i20882701/7b14bb94faea46f9.png)
![](https://img.haomeiwen.com/i20882701/40d9261266b06bef.png)
//对称区间,想到偶函数,所以只需要证明一边。证明过程巧用不等式避开了二次导数
![](https://img.haomeiwen.com/i20882701/816b3c0861a5ba7c.png)
使用拉格朗日中值定理推论去证明等于常数:导数等于0,区间内点等于常数
![](https://img.haomeiwen.com/i20882701/3f82f01a16266f23.png)
![](https://img.haomeiwen.com/i20882701/64eb5880ec675070.png)
![](https://img.haomeiwen.com/i20882701/2a7143a075292d63.png)
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