解题方法
1 . 已知函数
,
.
(1)求
的极值;
(2)证明:当
时,
.(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b923fcc6830f02925f594edcb9fcc90c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d6bcf1135449e1c9bb97f6927aa55b3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08cd1568daf759620e6842d75d88d558.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9405361d7be3c9e4d462a4e955d8fe3c.png)
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2023-09-19更新
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2卷引用:陕西省西安市第八十三中学等校2023届高三二轮复习联考(一)文科数学试题
名校
解题方法
2 . 已知函数
,
.
(1)若
,求函数
的单调区间;
(2)若关于
的不等式
在
上恒成立,求
的取值范围;
(3)若实数
满足
且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87e9e05a32a98aca42cc47db6f3a81c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e0e6ff9703591326c139d89471aae4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cda591d3909af06eabf6b37c65bfe571.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0abc8a9262b5979278ea32021fd4abb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/731bdc8d2686a05f12a2ba8a7e3b01be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a32a311ca04cecf2defd9a8dbb617c.png)
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3 . 设函数
(
且
).
(1)当
时,求
的单调区间;
(2)设
,证明:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c47d7d4a2b278b0fbac180ef01a8075f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ffecb03c47be920254c4ccffa5b222.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047056c99b39c70fa40d3c8178e5b631.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71baf6217604517fd98fa97d0f55b43.png)
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2023-09-08更新
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3卷引用:陕西省、青海省部分学校2024届高三上学期9月联考理科数学试题
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4 . 已知函数
.
(1)若
在
处的切线与
平行,试分析
极值点的个数;
(2)若
有零点,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a20e8dd2e0de7a2efdc9337c6d21885e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6982f2268e3a563e7fbd3cd58a2eaf0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffc122f630d6c809acadea5380218785.png)
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名校
5 . 已知函数
.
(1)讨论
的单调性;
(2)当
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70566518997abd6bf0afabe06807b785.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c11cf3ca4a89057b9e7a11be36ac7bed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48b8da5de0594db80f92dfcbe857b537.png)
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2023-08-27更新
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5卷引用:陕西省2024届高三上学期第一次联考理科数学试题
陕西省2024届高三上学期第一次联考理科数学试题广东省部分学校2024届高三上学期8月第二次联考数学试题河南省洛阳市洛宁县第一高级中学2023-2024学年高三上学期第一次月考数学试题黑龙江省大庆市2024届高三第一次教学质量检测数学试题(已下线)考点20 导数的应用--不等式问题 2024届高考数学考点总动员【练】
名校
解题方法
6 . 已知
,曲线
与直线
相切于点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
.
(1)求
,
的值;
(2)证明:当
时,
恒成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2c6963d0dc385e75724ac0631a552d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4022404158a19da85fe55773ebd331a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e7812047c6a1b902cd9d40545d09731.png)
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2023-07-20更新
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5卷引用:陕西省延安市宜川县中学2023届高三一模文科数学试题
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7 . 已知函数
.
(1)讨论
的单调性;
(2)当
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bab9295ba157e91ee01a2083b755a049.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31467e7c6f18e972dd8bb886cb6d4cc5.png)
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2023-07-15更新
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4卷引用:陕西省宝鸡市陈仓区2023届高三二模文科数学试题
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解题方法
8 . 设函数
的图像在点
处切线的斜率为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8ce99d5fb0d69a2f790b1a84abb3fbf.png)
.
(1)求实数
的值.
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07abf4bd858ef1fa3e0de2cb70eb839a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2763b57a7399653fbded5264f0cee150.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8ce99d5fb0d69a2f790b1a84abb3fbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc688d0cce1585f46a25e830ada2cd48.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22b0580106025f517ca2cda8bf675ca2.png)
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3卷引用:陕西省商洛市镇安中学2023届高三下学期模拟考文科数学试题
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9 . 已知函数
.
(1)求曲线
在点
处的切线方程;
(2)设
,求证:当
时,
;
(3)对任意的
,判断
与
的大小关系,并证明结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c38e2cfb9e16f2f5d7a1e9a7590dd073.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68c6b6a11760d0724b0b60e55970e229.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/585de67a3fc494297d375d339af6d153.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b79ae1ceee652b06fc889607ff3f1df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fa38ca27c6c0c40d5e36b2ae4fb7ba7.png)
(3)对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c975a637794e6be6dd95e1e1ba12620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baa9fca7538f46d9d2b4429dd085ac78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d4fc8faefb26b233d4aa9dbef043aae.png)
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10 . 已知函数
,
.
(1)求证:
;
(2)若函数
在
上有唯一零点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ead46bb1895b5e4ecdca910c8185d99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d752d8db8a05b3ec7312f6ac8b64a07.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/612b09e53cffcbe930e37b038b2057cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ffd1f6bd3686a07efa4086a02b96a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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