名校
解题方法
1 . 若
,关于
的不等式
恒成立,则正实数
的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36fac79eb549c72549f3718d0c80bc92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2024-05-30更新
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1344次组卷
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3卷引用:广东省广州市华南师范大学附属中学2024届高三下学期高考适应性练习(4月)数学试题
广东省广州市华南师范大学附属中学2024届高三下学期高考适应性练习(4月)数学试题(已下线)第3题 妙解指对函数最值(压轴小题)山东省菏泽市定陶区第一中学2023-2024学年高二下学期5月月考数学试题
名校
2 . 已知函数
,则下列命题正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c44b295fec512c964da60e5e409a998.png)
A.若![]() ![]() |
B.若![]() ![]() ![]() |
C.存在实数![]() ![]() ![]() |
D.存在实数![]() ![]() ![]() |
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名校
解题方法
3 .
.
(1)若
的图象在点
处的切线经过原点,求
;
(2)对任意的
,有
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc75d573a99fb4f11396d28bc2eed586.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afd3ffc5e95e5f22723402501c9916b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(2)对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac4cbc7b067862a3d9c6789b392fc068.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52096e4e09e4924f722ec78f3cb7fe41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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4 . 已知关于
的不等式
对任意
恒成立,则实数
的取值范围是___________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af34fa130c976150970d9da1bb21b56f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e95ab6ce2369fa5338d1fa5589bfbc96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
解题方法
5 . 已知函数
.
(1)求
的值域;
(2)求证:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d85891847e4fce1951f0eb6a5c696c5.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c768e5a8a2c72590a83fb7f0b2f10475.png)
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名校
解题方法
6 . 已知函数
.
(1)当
时,求
的极值;
(2)当
时,不等式
恒成立,求
的取值范围;
(3)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6ec28f8c49a8ec27cb4140096eda5c0.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/521976f4b831d5e16926de504af83567.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/636289ad84b4a3a51095dd32ca201f94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d16a27b4a2c205a71f97ebfb6dde5d84.png)
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解题方法
7 . 已知函数
,其在
处的切线斜率为
.
(1)求
的值;
(2)若点
在函数
的图象上,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c074042b84baa341258b1e701e1aea7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29d437fc0f48ceb7b5b9bcef34e3448c.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a64d924836b4292239d9726c6473d7f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86eb59d57b46c345081ecf1317f5f27c.png)
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名校
解题方法
8 . 已知函数
.
(1)当
时,试求函数图象在点
处的切线方程;
(2)若函数
有两个极值点
、
;
(ⅰ)求a的取值范围;
(ⅱ)不等式
恒成立,试求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cdcd099fd8cc0a68212f70af3d9fedc.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffd888afdcfdb3e91a157d50f65e915e.png)
(ⅰ)求a的取值范围;
(ⅱ)不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1f9fa86fe5015298d7ef9f51cc31207.png)
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名校
解题方法
9 . 设
均为正数且
,则使得不等式
总成立的k的取值范围为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c14d9ae06f864498048d55088ff4e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb8d26087a321c3276225c55f2829764.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23dced4c4dfdec458b4d7319ee75d51f.png)
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10 . 已知函数
.
(1)若
,求曲线
在点
处的切线方程;
(2)若
在
上单调递增,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24f877480423527e33b3418f1a8d6259.png)
(1)若
![](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/1b5a02983315012227085c59744aa621.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99f68c6ed09e483db6edf0b4caf5e252.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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