1 . 已知函数
.
(1)求函数
的单调区间;
(2)当
时,关于
的方程
有两个不同的实数解
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d2d36bf6438aa2ec7464f7106c83b50.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/558c89b5e71802cb56750846970db46b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c390e719e9e80b006ca63306139bd112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31eceb72067283ab655fbb1783303f20.png)
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2019高三·全国·专题练习
2 . 已知函数
.
(1)求函数
的单调区间;
(2)若关于
的方程
有实数解,求实数
的取值范围;
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32d43849618da5f227124186a9085944.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b55b22fd2e3f3b4c6cb424b535067a2.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed9af8c3fbdb748fd11e2423de063616.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eec837ec00020d0b48ebf6f16ee82fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b61ed9fd6fbfbea7a406c80a7b92df8.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9fd4f67253d2d145dc477d34677b191.png)
您最近一年使用:0次
2018高三下·全国·专题练习
解题方法
3 . 已知函数
.
(1)求函数
的单调增区间;
(2)若
是方程
的两个不同的实数解,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87db5ca3e18b18b813e00a7221d39580.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c342d52fc26cc550a45b80756903bee6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f15c88945a9a3ea4cb023949ae04d6c.png)
您最近一年使用:0次
4 . 已知函数
,
在
处取极大值,在
处取极小值.
(1)若
,求函数
的单调区间和零点个数;
(2)在方程
的解中,较大的一个记为
;在方程
的解中,较小的一个记为
,证明:
为定值;
(3)证明:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5b9786691166ee37475c593fba6636.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb788ae88e457017bb81120b6a2e5ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b12a4eecd249473a831d0ee472470240.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9565876bc50bceb63e5793c8c67a9032.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1487e9e4bd2c25c594e655e95c44d574.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb788ae88e457017bb81120b6a2e5ee.png)
(2)在方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d46db6ccb3adc70100e1c581f606157c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ec13d0c7a2f811a742d7e89960c5fec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d30c926f1a866b6c67b44f14e6018359.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/361b11b445f4801ef928a198c8b46273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b75c42450d4c9cb1a19e34f03a4bc18a.png)
(3)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1403d67bf7315f6869255bbac7060f65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb2d9a8239618fd3d2d026ae639a2a80.png)
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5 . 已知函数
.
(1)若
在点
处的切线与直线
垂直,求函数
的单调递减区间;
(2)若方程
有两个不相等的实数解
、
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0047d362cb6258ef84353772030d551d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38bf1acd09e90a6fbd1128da062b38ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f281814a940820e52ec332185871e22f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907e4ba6d5f2eea68442def1911957fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/546a1ee9369c1c238e3e9ff1bb4a236e.png)
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6 . 已知函数
.
(1)当
时求函数
的单调递减区间;
(2)若方程
有两个不相等的实数解
、
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0047d362cb6258ef84353772030d551d.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907e4ba6d5f2eea68442def1911957fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39a533560863efecd642f0476fe8a38.png)
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10-11高二下·浙江嘉兴·期中
名校
7 . 设函数
.
(1)求
的单调区间;
(2)当
时,若方程
在
上有两个实数解,求实数
的取值范围;
(3)证明:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f8b2498cc8d16d541af5c040f86ea25.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/976d18a5396ba232f0aa38d136f1d749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc548dc9512f29922c422da279b3de18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(3)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66eba129d92ede31b728e2590c4db2a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e84757ffc2970361793a962d20eb026.png)
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10-11高三·四川南充·阶段练习
解题方法
8 . 记![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7cbdbbc8ba5e423059869ae9c4ef089.png)
是
的反函数,
(1)若关于
的方程:
在
上有实数解,求实数
的取值范围;
(2)当
(
是自然对数的底数)时,记:
,求函数
的最大值;
(3)当
时,求证:
(
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7cbdbbc8ba5e423059869ae9c4ef089.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(1)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32915ef64ef42f9aac6b3d5ce054aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04614d0fac9cde995374a43d4323b723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b7393fc425948d4261bb6c7d67f88e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d71bd4fc36f62c1a9fdb1775f5c35c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7df943cb0ed70aa83183c354d29d874.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
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9 . 已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c20848891163f6f11e121fc7fba310d9.png)
(1)求
的极值点;
(2)当
时,若方程
在
上有两个实数解,求实数
的取值范围;
(3)证明:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c20848891163f6f11e121fc7fba310d9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/713c59f274e9146b6d85375435315521.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/298873fbaddfa54307878a9c57bcf154.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(3)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66eba129d92ede31b728e2590c4db2a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aab05316c010d6dba95f74749dd588.png)
您最近一年使用:0次
2012·河北唐山·一模
10 . 设函数
.
(1)讨论
的单调性;
(2)( i)若
,证明:当
时,
; (ii)若方程
有3个不同的实数解,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2beb9de9d7aa2ee49bcc5fe32348456a.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)( i)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cb595535eaefe630a624adc02b713fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9351efff43e9446744faa1ea599dfc1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c342d52fc26cc550a45b80756903bee6.png)
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