解题方法
1 . 已知
.
(1)若
,求b的取值范围;
(2)求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe6d9480b686da380941a1a4e2ee9d93.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3ab573d12140a6c3bd663cab95c270a.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b18e8e45c5b91a21978a9f9cfcf1886.png)
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2 . 已知函数
,m为
的最小值.
(1)求m的植,
(2)已知实数n,p,q满足
,
,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63502808190adaeb97a37a0f4eee1d29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)求m的植,
(2)已知实数n,p,q满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59b2400d72b1e3145cb21ba719d8a968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a3ac83c571110d41a396d12d8eea1c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6526e19f5af4425fa017e3d38c42116d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235953c833fc96e4ce88e17051aef93c.png)
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解题方法
3 . 已知
.
(1)求
的解集;
(2)记
的最小值为
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c00c196c040e330a18551d161627aadc.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94cc25a7cf28ed096549fbae97fce40a.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d30e4faeb8359c0e72f10f01842848c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b73ac9f6c8592e734954588e85a8cec.png)
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4 . 已知
,
,
均为正数,且
.
(1)是否存在
,
,
,使得
,说明理由;
(2)证明:
.
![](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/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a57e060f61f7efa54982bda67db483a.png)
(1)是否存在
![](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/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5882aba406145a4755d3bc184b8aee30.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31270f0a9cb69c97225271fb354847db.png)
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5 . 已知函数.
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48adb8a59b5c02fad5eada1b35171cf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fbc901cbdb68130ddac3174583dd93c.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a7dbc702617c765a573961953cc0901.png)
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6 . 已知函数
,
.
(1)当
时,求不等式
的解集;
(2)当
时,函数
的最小值为
,若
,
,
均为正数,且
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d6432b29955afe5c6e53b27ab24422c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6acb0f1ac694dd177e99fc385f23318.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.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/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143c384e3ed4f411015eadb97737fbfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3189d64f0b0a888709e75d459f110168.png)
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解题方法
7 . 已知函数
.
(1)求不等式
的解集;
(2)设函数
的最小值为
,若
且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/113eff4fc6357344d826ff081714339d.png)
(1)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3a075dce77c9a6b964a8a3fc1ee6e8c.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd517c952785f1b4a87a0ff47260e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2684b72f9f38f5046c8ecd4280b7b14b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/711d33dca588abbd3e2bead7ec99a384.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/576e3d63873b53cc17f79139e674308b.png)
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8 . 已知
,若
的解集为
.
(1)求实数m,n的值;
(2)已知a,b,c均为正数,且满足
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae822f6e0ed760e5de7216a674ace1f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ec4add31dd4c2d48aadbb7bd13e607.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4617ae497c70e9aa68d601da1d7d9b5.png)
(1)求实数m,n的值;
(2)已知a,b,c均为正数,且满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdf369f25d8767c656c2a8ef2c00d9bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41b1672ae944369491164bb952ab8873.png)
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9 . (1)已知a,b,x,y均为正数,求证:
并指出等号成立的条件;
(2)利用(1)的结论,求函数
的最大值,并指出取最大值时x的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7381cf2d8df0ec7f569046d580d40a1f.png)
(2)利用(1)的结论,求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3b13d632379fbe54d0c957d1d14329e.png)
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解题方法
10 . 已知函数
,
.
(1)当
时,解不等式
;
(2)若存在
满足
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb233e811cbca49a9c356f0de5c37aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcd9218a657b17654c5d757a6f7dee9a.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8a3cc8c48bf54ec8252e5dce6867754.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e2405c4822bceae1cf191edb502d3b0.png)
(2)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06984e87f4329684aa461656f5de1f1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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