组卷网>知识点选题>利用导数证明不等式
显示知识点
显示答案
| 共计 2181 道试题
1 . 已知函数eqId4f348a91d14b49519457995a4dded013eqId5ede944e7ec047a980b3db502ec3cbb9,其中eqIde9edd995034840cfb557ea415074294a.
(1)当eqId37303db52eae469a99849374b5331b25时,求证:eqIde7f142cb18b84a25b84f2994e07b9209
(2)若任意eqIdcf1d255cba78458f98f39ef5d0706790,恒有eqId9279c43ee06e42daab22b78403b218c8,求实数eqId70a27b6ddf6b478285353abb3b1f3741的取值范围.
解答题 | 较难(0.4) | 2021·常熟市中学高二月考
2 . 已知函数eqIde02a1b1654ec4a1cbca62cd7abc2607ceqId982da3835b7946d999cc8604a2ece266.
(1)若eqIde4a0e3706b56447b90fe1b2781f91b14为单调函数,求a的范围.
(2)若eqId735b8047beee4dee870fc72ae837a245eqIdecaaaffea9af458c8e6dff16f15c1a73函数eqIdbbc4df94a65b4983bd36e80b8cbaa4ab的两个零点,求证:eqIdf64a568dfc2d491bb7beda351a032673.
3 . 已知函数eqIdf4533eae6fd64a35b7b14ade46ce640d,若存在eqId735b8047beee4dee870fc72ae837a245eqIdecaaaffea9af458c8e6dff16f15c1a73eqId1e1239902cd74ecca8f54d82b6dae404),使得eqIddca89a9ef93642c6bffa3c3fb60fbdad
(1)求实数eqId69f56ef2c88b4b73a560da59f5247a82的取值范围;
(2)证明:eqId871a73efff52495f8cf74345d75a8303
5 . 已知函数eqId4fc170a361174c10ad9f9558171117e8
(1)讨论函数eqId6f13759e937144069819aed2ae5a1057的单调性;
(2)证明不等式eqId467e7798090840a98dd69775bf2e245f恒成立.
7 . 已知函数eqId7618ef845c42486e83f2fa794cf31c16k为常数,e=2.71828…是自然对数的底数),曲线y=fx)在点(1,f(1))处的切线与x轴平行.
(1)求k的值和fx)的单调区间;
(2)设eqId0ff2c0a5328c49b38794982f8bf1e830,其中eqId8a8df962ce714add890ad66f40444da7fx)的导函数,证明:对任意eqId70a453585cdd4dadab5f453009262262.
8 . 已知函数eqId35b7561419c2495bb8374471c7609c3c
(1)若函数eqId6f13759e937144069819aed2ae5a1057在R上是增函数,求实数a的取值范围;
(2)如果函数eqId70fe90ec3194459faf63e7c4bb551340恰有两个不同的极值点eqIdca06d7ef3b984e8c8fb8f7d217749d05,证明:eqIda68f97fbeda240b8baeae01a171dd0a5
9 . 已知eqId50eeca3d06c64378b11fce6439f4b1b4
(1)对一切eqId94a99efcc8d54739b6444f390bde7ca7恒成立,求实数a的取值范围;
(2)证明:对一切eqId45f4ca0a3e5c4a4fa9585073df543039,都有eqId747bebef56bf4306878ab9ad20b28e28成立.
10 . 设函数eqIddd3dc59a4dbd430290d680d4cae05cb8.
(1)若函数eqId6f13759e937144069819aed2ae5a1057的图像在eqId90f4010cc71b4998be6fa90952078f6b处的切线平行于x轴,求aeqId6f13759e937144069819aed2ae5a1057eqId7866cdd713694d23943f903588364452上的最小值;
(2)当eqId982da3835b7946d999cc8604a2ece266时,设函数eqId6f13759e937144069819aed2ae5a1057的最小值为eqIda364cbeebde9457196cdc80861bdf57e,求证eqId957ef44961754c3b9acbacda48e4ac03.