组卷网>知识点选题>构造函数法解决导数问题
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1 . 已知eqId55c48e51baa64c17902bc89170e7d0f6eqIdc59165a9547d4f38b99449a2ad322ee0eqIdf035b8f27d4645bb9f6a66f4a3f51918是自然对数的底数),eqIdae25678e93714c8d9c5c0e9d9efabb0e,则eqId70a27b6ddf6b478285353abb3b1f3741eqIdaea992e70d4943e49e893817eb885ed7eqId44925af6fb19413689ba5616e3647cba的大小关系是(   )
A.eqId5abec93a81364603bfbf23b3f73cd1a4B.eqId0d0cc8a6003c4e21bacd608a53c711cfC.eqId98df60d61acf40a38ea6e88af8316379D.eqId45615ef0900647268b98d1d5eeb28a58
2 . 若eqId84baf5260a714df9a42e9e3daf01ca4a,不等式eqIdeb0f4ffaa2ce4242818291296200f04deqId68f73587123947aba24aeda2e00fec2c上恒成立,则实数eqId70a27b6ddf6b478285353abb3b1f3741的取值范围是__________.
单选题 | 一般(0.65) | 2021·湖北孝感市·高二期末
3 . 已知定义在eqId7dcd2312d0bf4bb1befdfcc170e45791上的函数eqId10852d81bc184140a7780250c82c6929,其导函数为eqIdd26cd9f8ad374ae192a20aada45c1618,若eqIdd68b11dc5abb4dada26dfe83daa97212eqId48252f1841a34ad183c4c75ed5985324,则不等式eqId54d30e69014248119522f6df15327d13的解集是(   )
A.eqId8db787b1fecb48d9a410efd47c7a8118B.eqId68f73587123947aba24aeda2e00fec2cC.eqIddca4c31f92e1447fb6eceb9fdf294175D.eqIdcd23deec614f478589b5ff357029ae50
4 . 已知函数eqIdf815dbfb6c01419e824ff02243cb16cceqIde9edd995034840cfb557ea415074294a,曲线eqId144eff5c0e4649138a21f2b1b6a06907在点eqId0b1b4db05c2b4383b710e7d505a3605a处的切线过点eqId901b74730471488691d522bfd5045640.
(1)求eqId70a27b6ddf6b478285353abb3b1f3741的值;
(2)若eqId6f13759e937144069819aed2ae5a1057eqId02b4fd87b6dc469297673255c63eed1c处取得最小值,求eqId2a26379f02914b9b8415d5e7a52fff1c的值.
5 . 已知函数eqIdf6501952a90c4cc0945bc3ae0f9bee11,且eqId9efc4f6e4453489fbd49d2c5f340bd81
(1)当eqIdba00dd4af19048d7a97e6f1a3882db2b时,求eqId4837c94ef0ff4dcf9b1dda4df363275a的单调区间;
(2)在函数上是否存在两点eqIde8e523c405ae45c19676ed23f0cef311eqId55cba36c462f4746af6690bf1ac89881,使得函数图象上在eqIda721530773ee419a8ec1df1d95784e68处切线与eqId99a3187c2b8f4bcc9703c74c3b72f1f3所在直线平行,若存在,求出eqIdeb53cb7cb0274f7d8f111c60f824c243的坐标;若不存在,说明理由.
解答题 | 较难(0.4) | 2022·全国高三专题练习
压轴
6 . 已知函数eqIdecad957cc1c24285aae917092b12dbb9,其中eqIde9edd995034840cfb557ea415074294a,令eqId9c9fcbe67c494a568f43557284945730
(1)求证:当eqIda53c997ffb1244b284bf1503b67d6488时,eqIdfcaf3bbe14e548cc8d47beb2467db5a0无极值点;
(2)若函数eqId6412a27f0512412e826aaf38a7751761,是否存在实数eqId70a27b6ddf6b478285353abb3b1f3741,使得eqId35f0efe769ec417999184e899886ad69eqId90f4010cc71b4998be6fa90952078f6b处取得极小值?并说明理由.
更新:2021/07/30组卷:0
解答题 | 困难(0.15) | 2022·全国高三专题练习
7 . 已知函数eqId9c13ff0b6687441f8900169d6d88ae82.
(1)若eqId6f13759e937144069819aed2ae5a1057eqIda9d8558290c64896b00f1c4577d0d92f处有极大值,求eqId70a27b6ddf6b478285353abb3b1f3741的取值范围;
(2)若eqId6f13759e937144069819aed2ae5a1057的极大值为eqId2381423d4cd146cab95f55527681a766eqId6f13759e937144069819aed2ae5a1057的极小值为eqId517584fed25c413ba8b7bb33ffa2d5c6,当eqId8073b8f262314441ae8dfbbb6c223459时,求eqId78ea38c2138a41409c04b79ac2d89945的取值范围.
更新:2021/07/30组卷:0
8 . 设定义在eqId7dcd2312d0bf4bb1befdfcc170e45791上的函数eqId144eff5c0e4649138a21f2b1b6a06907满足任意eqId6fc94f6e181444c6b809fb393eb8fae6都有eqIdfb92594777ef42a8ae6840623e18a974,且eqId87843564b5f74108a78b22f4551a039c时,有eqIdd77c8fa8042e48919fc327f786c948ff,则下列大小关系正确的是(   )
A.eqId805175ff191c4d1e8036ed20c963c4ea
B.eqId4b7b3c6e6e6a4f829b85bc6954ea78d2
C.eqIdb46c845cb5f540e180deed03c647cffa
D.eqId8f1d654450f94f73bd43d206988afca3
9 . 已知定义在eqId38a1a72a865d4179b3b243977e23dce4上的奇函数eqId6f13759e937144069819aed2ae5a1057,其导函数为eqId39f6d0ac61bb453890de392f136c3074,当eqId2d569479cd1c43c1af15895792b64db6时,恒有eqIdad30b9f1a77844fe868c378126a0c8ab,若eqIdfc8d996dbeca4d1f9d936d0adede0343,则不等式eqIdba82b3b4b55448488fc0345ec4ed33d1的解集是(   )
A.eqId880f8b086d874bb3a039cd4d25019e50B.eqIdb01893c11ede441dad1b602ece47a374
C.eqId92e73e2b41904318ab5e3d5894a91e80D.eqIde327c47000b04c6daee727c47be19120
10 . 已知eqIde4a0e3706b56447b90fe1b2781f91b14是定义域为eqIddca4c31f92e1447fb6eceb9fdf294175的非负可导函数,其导数eqIdd26cd9f8ad374ae192a20aada45c1618满足eqIde6393b14c9884e94bbfbb8a441b3299a,记eqId265cfa2a0c38402ca917f059a6f1565eeqId722b86c4864943b8b821f03681a93c83eqId5cdf0fa81a9b427b941abd5807655842,则(   ).
A.eqIdc08d7b308c78467d8f8413824674b10dB.eqId4d05312df11244ea958dc5bfa677c103
C.eqIdf7fadb0bc1554becad52e0e5f328862cD.eqId5e94e92dc6ab4139815085e9e4f482c4
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