名校
1 . 已知函数
有两个零点
,
,则下列说法:
①函数
有极大值点
,且
;
②
;
③
;
④若对任意符合条件的实数
,曲线
与曲线
最多只有一个公共点,则实数
的最大值为
.其中正确说法的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/620809df01729bc526807d556a5e2b65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffd888afdcfdb3e91a157d50f65e915e.png)
①函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31cdc61764eef3fbe2dc5fafaa2efb39.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b4900c67f4b57fa430c4bd863f8e896.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d406c2022d92072bd3f4a93d0e472c82.png)
④若对任意符合条件的实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbd661503039022b395ff97b9d91aa66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c2df754f77604928c25690dde22b753.png)
A.1个 | B.2个 | C.3个 | D.4个 |
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名校
解题方法
2 . 对于函数
,如果其图象上存在不同的两点
,
,
,使得这两点处的切线重合,那么我们称函数
存在“双切点切线”.已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5eb25153f05e68b3368495d2b0a4747.png)
(1)已知函数
的一条“双切点切线”的斜率等于1,切点
、
的横坐标
,求实数
的值;
(2)如果函数
存在“双切点切线”,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45dddee525114c09ee0d1205aed6e7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b3b54e0dcdc081d45fb3df933cddc29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84b5f32c09caa0be0d4c33be07aa4530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5eb25153f05e68b3368495d2b0a4747.png)
(1)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.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/4a7b0c34c4a6e7be6f08ef7b7829c4b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)如果函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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