组卷网>知识点选题>利用导数解决函数的极值点问题
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1 . 设函数eqId3d25baeadb2447a0a5308f24c7c9d35deqIde9edd995034840cfb557ea415074294a
(1)求eqIdd26cd9f8ad374ae192a20aada45c1618的单调区间
(2)已知eqId10852d81bc184140a7780250c82c6929eqId90f4010cc71b4998be6fa90952078f6b处取得极大值,求参数eqId70a27b6ddf6b478285353abb3b1f3741的取值范围.
2 . 如图是函数eqId9b37d03e47a347fc8fab9f814ba5fac4的导函数的图象,下列结论中正确的是(   )
说明: figure
A.eqId10852d81bc184140a7780250c82c6929eqId77c0d933bf1f4361a26d0747602918bf上是增函数B.当eqIdbf6df677a4ad4645b9eb2dfab9d3230f时,eqId10852d81bc184140a7780250c82c6929取得最小值
C.当eqId304afd9f2ec84e138ab539275a5edd19时,eqId10852d81bc184140a7780250c82c6929取得极大值D.eqId10852d81bc184140a7780250c82c6929eqId510fabb288f048fdb2fca37a08e82cff上是增函数,在eqIdf173839cbdf549429066610d1a327f06上是减函数
3 . 已知函数eqId29d51e574ed343c8b3bd0ea73f2d5e8aeqIdd5a6569623204652aada8c497a766e0a处取得极值A,函数eqId76d2d768c7ab4a8db243a83c54536f75,其中eqIdc2487b58a3a3457c8a59a9e3548ff1b0是自然对数的底数.
(1)求m的值,并判断AeqIde4a0e3706b56447b90fe1b2781f91b14的最大值还是最小值;
(2)求eqIdd077167f12154199a0f30bcefb739eb5的单调区间.
4 . 已知函数eqId3603be6ded804f06b6655c1f18132925.
(1)当eqId83852d75044b4ef6a65c857a110b59bb时,eqId6f13759e937144069819aed2ae5a1057在点eqIddd84fba5c68c4651b7a3fb0f8be92c90处的切线平行于直线eqIdb545805bdae44bc4b4d7e1264caead7f,求eqId70a27b6ddf6b478285353abb3b1f3741eqIdaea992e70d4943e49e893817eb885ed7的值;
(2)若eqId6f13759e937144069819aed2ae5a1057在点eqIdd4bd920782f24ef09cad69bfced77954eqId06b46be315364cbc87dce508a946e30c处有极值,求eqId6f13759e937144069819aed2ae5a1057的表达式.
5 . 已知函数eqIdc6c778a256ba47cca49cb84c85badf56,其中eqIde9edd995034840cfb557ea415074294a,若函数eqId6f13759e937144069819aed2ae5a1057eqIdd5a6569623204652aada8c497a766e0a处取得极大值,则eqId783c5f01aa1e49b29f88c27d2eca4354__________.
7 . 已知函数eqIdc0510cbc4f9b41a1bdbf44069e2db466,则下列关于函数eqIde4a0e3706b56447b90fe1b2781f91b14说法正确的是(   )
A.eqIde4a0e3706b56447b90fe1b2781f91b14eqId9c4f56b428bd4a5c947d36cfcedceddf上单调递减
B.eqId29c898c2f6d5480e84ed6cd0dfc0930beqId8898c1dc81824f3098bbeae74e8f11fd是函数eqIde4a0e3706b56447b90fe1b2781f91b14的极值点
C.若当eqId6c75cfc8b2e6448999c11a39cddbcbeb时,函数eqIde4a0e3706b56447b90fe1b2781f91b14的值域是eqIde5faa99210804831b30bb60b883157b8,则eqId3603f87908254846bf03a58b40253b1f
D.当eqId4b11f13bf285431aa7c5dd3c713d974e时,函数eqId08cf7a4817eb4b16940d14a12ae91429恰有eqIddd4bf187d3fd47f6bcc24e568e09643e个不同的零点
9 . 下列四个函数中,在eqId90f4010cc71b4998be6fa90952078f6b处取得极值的是_________
eqIdea599fd639cb4dd8be5124de99252fd4;②eqId0c450d8f660147c4a94279f3c928b33a;③eqId60570a36f29c4a1baf99bf04ea0fb06d;④eqIde23355f6cfe94cf3870a9c3dffe1618d
10 . 已知函数eqId6f0811dce9ee4672af1e08ecf9604a44eqIddbfe2296ba394f0b8b5d056fc8d92060
(1)当eqId37303db52eae469a99849374b5331b25时,求eqId10852d81bc184140a7780250c82c6929的单调区间;
(2)若函数eqId4bde1d78f6ef459f828041fd784da9d2 存在极值,且这些极值的和大于eqId6bdb736b48c5473dba1e674d27e71481,求实数eqId70a27b6ddf6b478285353abb3b1f3741的取值范围.