名校
1 . 已知抛物线与双曲线
交于点T,两条曲线的公切线分别与抛物线、双曲线切于点P,Q.
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb5261a9730779339dc71818b9b6eff7.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb5261a9730779339dc71818b9b6eff7.png)
您最近一年使用:0次
名校
2 . 已知函数
.
(1)当
时,求出函数在点
处的切线方程.
(2)如图所示,函数
图像上一点
处的切线与函数图像交于点
,过
的切线
(
为切点)与
处的切线交于点
.问:三角形
是否可能是等边三角形?若是,求此时
的值;若不是,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/144374b31db4198d359833cd7aa68f67.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d06e33d079ac1649ee5eea8f61de7cf.png)
(2)如图所示,函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
解题方法
3 . 我们把底数和指数同时含有自变量的函数称为幂指函数,其一般形式为
,幂指函数在求导时可以将函数“指数化"再求导.例如,对于幂指函数
,
.
(1)已知
,求曲线
在
处的切线方程;
(2)若
且
,
.研究
的单调性;
(3)已知
均大于0,且
,讨论
和
大小关系.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/541b679b72673528f0e37bfeb6d1dff0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f46d3504fd4d99c1a9a293a9363256ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52fc4b04f98545b403a28d41c6e109c4.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7395df460e74ac91beeb82f99bf301ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/060e7930731eddbcfac592b808e9b698.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b91f5cf5a5fede52e96a0cb5ac079b.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/607ea0d316d84b1ea5e6e735ac29b332.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2958030ec9d7543dda1f529593a915e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a94933201271f9408e70cd2f2182f4a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c632bdc4a2b1c4891d1cf5345571d23.png)
您最近一年使用:0次