组卷网>知识点选题>利用导数证明不等式
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解答题 | 较易(0.85) | 2021·全国高二专题练习
1 . 当eqId2d569479cd1c43c1af15895792b64db6时,证明:不等式eqIddeb9a999e6aa47b6a91c747773abccad.
更新:2021/06/14组卷:0
解答题 | 一般(0.65) | 2021·河北衡水市·高三其他模拟
2 . 已知eqId944d2222c6da4cfab0a6906cdd82c9c1
(1)证明:eqId0836c1003605494a89734a73b75e144c
(2)证明:eqId7bc4b6a948a84f60b850db163b4e879b.
解答题 | 困难(0.15) | 2021·浙江金华市·高三三模
压轴
3 . 已知函数eqId1df9e6cf07334df2bac78bc2ffd60ea2.
(1)求f(x)在点(-1,f(-1))处的切线方程;
(2)若方程f(x)=b有两个实根eqIdca06d7ef3b984e8c8fb8f7d217749d05,且eqId69154b0cb5e843698c5ea5bf0d8bdfa8,证明;eqIdc9981b9d811142749b54dc5c8a09a819时,eqId697984559d384e77ba45d189bb15fb15.(注∶e为自然对数的底数)
4 . 已知函数eqId01276a922788461fab7237f924043080在点eqId023079ae51b9456ba211bcf0b1900a46处的切线斜率为0.
(1)求a的值;
(2)求eqId4837c94ef0ff4dcf9b1dda4df363275aeqId318b26713a204fad8f58164bea88ad10上的最大值;
(3)设eqIdde7a3fa21eed48e6bc8d22fb492339b1,证明:对任意eqIde570e39985df45de987c67b35fd8c9bb都有eqIdf8ac2e9a5b7e4977b9473822e5c32fd7
5 . 已知函数eqId5f889442e0fd43bd9178184f5cc4e38f(其中eqId7fd12a1dccdd49bfb46543ccc297ec82…为自然对数的底数).
(1)求证:当eqIda73db392e835415db4f07895049ed729时,eqId5f4ee380d2c941b0b79ef2a7338ed546
(2)若不等式eqIdf5aa7d236090484d922f1331eda84f6feqIdb940e6eb1cb4452eb06eb321b9356056成立,求实数a的值.
解答题 | 较易(0.85) | 2021·全国高二专题练习(理)
6 . 证明exx+1≥sinx+1(x≥0).
更新:2021/06/13组卷:0
7 . 已知函数eqIdc1eebce200ab41c9b0e2f80eaae2bffa既有极大值,又有极小值.
(1)求实数eqId70a27b6ddf6b478285353abb3b1f3741的取值范围;
(2)记eqId735b8047beee4dee870fc72ae837a245为函数eqId4837c94ef0ff4dcf9b1dda4df363275a的极小值点,实数eqId4cf39834d9b34d24b0335cdbb9a5edb7eqId8d326959555a4bf49563449791dd72e9,证明:eqId40dd6a02e0a243d1b73e8fbd587f2a70.
8 . 已知函数eqIdd5740b615076465ead3713ba0c70506e.
(1)讨论函数eqId4837c94ef0ff4dcf9b1dda4df363275a的零点个数;
(2)eqId316e2199840e418e87252dba1d7d7ffd时,证明:当eqId85eb53575dd34c888bbb489e15f1b57e时,eqId3fbbaf7ddaf645d794db36899bac6bac.
9 . 对任意正整数eqIda4be99d332154d13a4a6ed1ff6444fe7eqId5f904d1376ac4de7a7d6cfea92ff6981,定义函数eqId112a53863a9241a69adbe331b5721d4f如下:
eqId534303a5d6bd4552bd0362b80074442e
eqId8dd92b081ada47c18e75a9ad9dcdddcd
eqId6ca4d47715b341d0959507e8f98913d1
(1)求eqIdb4683c46069b4e758e58529514d5109d的解析式;
(2)设eqIdf035b8f27d4645bb9f6a66f4a3f51918是自然对数的底数,eqId532dc4d959024b79b546428f5856e5aaeqIdacdc831dfd5844f8a410a70f6e13973a,比较eqId0a1a3f32018b4e0aaeab48046fc53b82eqId23a31ce03ec24588825c46fa918a87de的大小.
单选题 | 较易(0.85) | 2021·江苏南京市·高三一模
10 . 已知eqIdf035b8f27d4645bb9f6a66f4a3f51918是自然对数的底数,eqIdf1470514d3384b7d8224a7712ab506bd是圆周率,下列不等式中,eqIdbb69e3ddadbe48169f4b6ad3d942e167eqIdb8c8cdafeb53446a91f6e414d44f6911eqIde889d88e46e746c7a3cb15f69032cee7,正确的个数为(   )
A.0B.1C.2D.3
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