解题方法
1 . 函数
对一切
均成立,则实数
的取值范围是_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/252d47aaf6eed142771c7c8c80c6a907.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2 . 已知二次函数
,且
时,
.
(I)若
,求实数
的取值范围;
(II)
的最大值;
(III)求证:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/331d5e308cd5469e0f28a8d75f79903f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88a6bea084567e3055f0e58499398a46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/366839b25310cb3168d411b1d5f73b06.png)
(I)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c8066f8ed959c1316358fcbf802b7a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(II)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3697b04b4b7bdd6c42b62b0ae7b6c3dc.png)
(III)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e020de76853a6fa9b9e3f41d84c42d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97d397a6e7abac0ad425289a017e4f07.png)
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3 . 已知函数
,其中
,
,
.
(Ⅰ)若
是偶函数,求实数
的值;
(Ⅱ)当
时,求函数
的单调区间;
(Ⅲ)若对任意
,都有
恒成立,求实数
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11976693acdf39ca341f1a2e115ba075.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
(Ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(Ⅱ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48adb8a59b5c02fad5eada1b35171cf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(Ⅲ)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7dbb416ec1ff1984a724a4f48bf692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c47545bd5310d9c5c8de5f64a2a6e2e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5aa200de40134d6c0c865a9bc7ecb3b.png)
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解题方法
4 . 已知函数
,其中![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
(1)当
时,写出函数
的单调区间;
(2)若函数
为偶函数,求实数
的值;
(3)若对任意的实数
,不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/679c4a781050db15fe8f6c6395c0f15f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若对任意的实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01adffb67cb43f25dbbf5b0a781455dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfcc6401b133bbd705bdef842328bded.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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