已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f54d8484946ce597535b7093f0157a4.png)
(1)若函数
与
有公共点,求
的取值范围;
(2)若不等式
恒成立,求整数
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f54d8484946ce597535b7093f0157a4.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6872d88575e22c791660a91790c2e4b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
2021·河南·模拟预测 查看更多[6]
河南省2021届高三仿真模拟考试数学(文科)试题山西省晋中市新一双语学校2021届高考模拟数学(文)试题安徽省皖淮名校2020-2021学年高二下学期5月联考理科数学试题(已下线)第31讲 必要性探路法-突破2022年新高考数学导数压轴解答题精选精练(已下线)第六章 导数与不等式恒成立问题 专题二 单变量恒成立之必要性探路法(1) 微点1 单变量恒成立之必要性探路法(1)(已下线)第六章 导数与不等式恒成立问题 专题三 单变量恒成立之必要性探路法(2) 微点1 必要性探路法(2)——端点效应、极点效应
更新时间:2021-05-20 14:35:40
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名校
【推荐1】已知函数
,
.
(1)讨论函数
极值点的个数;
(2)若对
,不等式
成立.
(i)求实数
的取值范围;
(ii)求证:当
时,不等式
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6225208da0f993459b1aa6cebf75e71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/824567f7737a62ac120b0dadc44e6263.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6422b9c2e93a91fe9e39ce4d9dabb0fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b4955c5adc717b7f6f0b975e0724ff5.png)
(i)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(ii)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd8e6ca571901c25b53f263d31184994.png)
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真题
【推荐2】设函数
(其中常数
).
(1)已知函数
在
处取得极值,求
的值;
(2)已知不等式
对任意
都成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27e08ae517f81a6809bce36374fab657.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da989240786ef7c3e2d903f30caf59e3.png)
(1)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)已知不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c026e72833b3bfa4e2a5ef54f09ffd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/664d9ee5169a59edafcf497e523ed3c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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【推荐3】已知函数
与函数
的图像关于直线
对称,函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aac0458c1675fa54e0baabd05b8e632.png)
.
(1)若
,且关于
的方程
有且仅有一个解,求实数
的值;
(2)当
时,若关于
的不等式
在
上恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2ce61e9137c7dd5082c60e03523a2ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb788ae88e457017bb81120b6a2e5ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad7e66aae2e0bc0d5b5a3ffa7e4d9221.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aac0458c1675fa54e0baabd05b8e632.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da3b740f48d5bb2ff4ecb012acd10b8e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b74110bc818c2f5a53d63451c5251eb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ffb694021b52653de5141ae27ba6d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d68a1e35485988545f62e148726793ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4887473a8091e1ef53a169cc9f211e3a.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6335e7579ada89f23c50c623874bf06a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ffb694021b52653de5141ae27ba6d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b62b3ecfb3e9d0c4aa68a481aadc1bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0982a7abc710a572a24dc5a04b041ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab4717e4827480f0f6f4ded85e52eab.png)
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【推荐1】已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04292dee056bb3cf176145bf616424fa.png)
(1)当
时,求曲线
在点
处的切线方程;
(2)在区间
内存在实数
,使得
成立,求实数
的取值范围
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04292dee056bb3cf176145bf616424fa.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ea9824af71c9da5db5a00ec06063024.png)
(2)在区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6c1756b564bf1d998d8179637011c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71baf6217604517fd98fa97d0f55b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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【推荐2】设函数
.
(1)若在定义域内存在
,而使得不等式
能成立,求实数
的最小值;
(2)若函数
在区间
上恰有两个不同的零点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf3473c109ec4d71f833dad76eb5d145.png)
(1)若在定义域内存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb8cedb5b1a2e65f3cd0163e40c63a2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09c32d8c45dc1b0dc71195f2da09c47b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5432187d1c042787433b7633292d00fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
【推荐3】已知函数
,
.
(1)若
,求函数
的极值;
(2)若
,
,
,使得
(
),求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d9b57d9da26ba452af7f9d832593776.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c52eedf05a052b678eef0ddc9ba071d3.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14afbfbf8417de57f2ea520649a7fc74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c7a09930b792ab84f4d31314c1d3df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/859b96cca5161f796f4cac489434b7ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0baedc4d7e690ab3f7d80d30ba0a9efe.png)
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