名校
解题方法
1 . 已知常数
为非零整数,若函数
,
满足:对任意
,
,则称函数
为
函数.
(1)函数
,
是否为
函数﹖请说明理由;
(2)若
为
函数,图像在
是一条连续的曲线,
,
,且
在区间
上仅存在一个极值点,分别记
、
为函数
的最大、小值,求
的取值范围;
(3)若
,
,且
为
函数,
,对任意
,恒有
,记
的最小值为
,求
的取值范围及
关于
的表达式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7dbb416ec1ff1984a724a4f48bf692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83a6c0fddb9074dfc96be03b4aa24d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1678002c227b520668ab2b976cdfaa3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79d79a8b8500b2313a5b08a023d90b15.png)
(1)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08b9f0b9e53a83e68f5fec944f343119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7dbb416ec1ff1984a724a4f48bf692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4bf72626042d976d413196215876684.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4c8381377b90826897eb4bf16cb3bae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7dbb416ec1ff1984a724a4f48bf692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01bea8bf593f594c51fc7cc547482bee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51e817f37f5a814e856ebc4a16d676ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71f6b7d80e4316967fdaea810895317.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ae7f07dbd9023f19556fe1e88414f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a1e0cac3f562e5b5b952b8231bb91c7.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fb2bc63bd8e38e371284aea1fb08861.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/572b3dcb438834635f79b2544934af84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c765461ae1a6c70f5cbdcb6c932a22b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3367bd41ff428d7a608511cfb1f3cb11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b97a0de833ddcd45995ff3286b5d266b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/760f804646698060703c5458ff5637c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/760f804646698060703c5458ff5637c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2023-04-20更新
|
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7卷引用:专题09 导数及其应用 压轴题(六大题型)-备战2023-2024学年高二数学下学期期末真题分类汇编(沪教版2020选择性必修,上海专用)
(已下线)专题09 导数及其应用 压轴题(六大题型)-备战2023-2024学年高二数学下学期期末真题分类汇编(沪教版2020选择性必修,上海专用)上海市徐汇区2023届高三二模数学试题(已下线)重难点04导数的应用六种解法(1)(已下线)第六章 导数与不等式恒成立问题 专题十二 恒成立问题综合训练(已下线)2024年高考数学二轮复习测试卷(新题型,江苏专用)(已下线)信息必刷卷01(江苏专用,2024新题型)江苏省宿迁市沭阳如东中学2023-2024学年高二下学期阶段测试(三)数学试卷
名校
2 . 设
是定义在
上的函数,若存在区间
和
,使得
在
上严格减,在
上严格增,则称
为“含谷函数”,
为“谷点”,
称为
的一个“含谷区间”.
(1)判断下列函数中,哪些是含谷函数?若是,请指出谷点;若不是,请说明理由:
(i)
,(ii)
;
(2)已知实数
,
是含谷函数,且
是它的一个含谷区间,求
的取值范围;
(3)设
,
.设函数
是含谷函数,
是它的一个含谷区间,并记
的最大值为
.若
,且
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c1486d2ae6c7e7904ab47b909039ba7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adadc4c82ed03710cb917d552ac6e1c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd33dd2e1b404daf7c1cbbf147ab7f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(1)判断下列函数中,哪些是含谷函数?若是,请指出谷点;若不是,请说明理由:
(i)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65ecb5b1f957213346a78a229314e73f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2323ed90e5321507ae65763db9594b9.png)
(2)已知实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2739d1d7a587d0a327c5b75fcaba9d5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7242b2ab643f9470da77e29d043b893.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e0137d9ccd136186c2fe74a11e42376.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f86c67af4135ba55b227485de51d4ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13502d46b8563c54c09b29b20b3006a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78b9c9a559b5ec35dd6bc7abf3f4c8d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c27aed40481d951cc4afd5c7c1a470d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94a112fefbaf48adf34edbf3243ee7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78b9c9a559b5ec35dd6bc7abf3f4c8d6.png)
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2023-12-18更新
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5卷引用:上海市浦东新区2024届高三上学期期末教学质量检测数学试题
上海市浦东新区2024届高三上学期期末教学质量检测数学试题(已下线)专题09 导数(三大类型题)15区新题速递2024届高三新改革适应性模拟测试数学试卷二(九省联考题型)(已下线)专题1 导数与函数的单调性(恒单调、存在单调区间、不单调)【练】广西南宁市第二中学2023-2024学年高三下学期5月月考数学试题
名校
3 . 设函数
.
(1)当
时,若直线
是曲线
的切线,求
的值;
(2)若函数
在区间
上严格增,求
的取值范围;
(3)若
且满足
,对任意的
,恒有
,求证:对任意的
,当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53e99b2155565e0832a2bc405cd29843.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9a9b769d70cb6f29e965c800921c8ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0e54c5da8061411e6659614a6511a30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca83d5dea2d5c02ac18a9c9496ca57e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1313a22f7070883f17d39700f383b504.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe276c0522839b1d37086d92612aa7c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc3d1fe6dd2ff21f192e14fd85062fb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d8deeaabea77488158d0a98639e02ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2958030ec9d7543dda1f529593a915e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af041a320a49a5db1828a26c0613ec89.png)
您最近一年使用:0次
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|
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2卷引用:上海市大同中学2021-2022学年高二下学期期末数学试题