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 . 已知函数eqId6f13759e937144069819aed2ae5a1057的导函数为eqId39f6d0ac61bb453890de392f136c3074,且满足eqId329b95fa9079496f8572e206b6549f47,则(   )
A.eqIde92b94023627458e854f0b6ef84eb0ba
B.eqId0dabed4866534edfac95e0475a00bc5c
C.eqId6f13759e937144069819aed2ae5a1057不存在极值
D.与eqId6f13759e937144069819aed2ae5a1057的图象相切的直线的斜率不可能为-4
2 . 设eqIde9edd995034840cfb557ea415074294a,函数eqId8a6e533650b9445b974776b8f7628b35
(1)若eqIda08ce385279d41c789695fb651b17890,求函数eqId9b37d03e47a347fc8fab9f814ba5fac4eqId90f4010cc71b4998be6fa90952078f6b处的切线方程;
(2)若函数eqId9b37d03e47a347fc8fab9f814ba5fac4存在两个不同的极值点,且eqId761b2917a82b4524b8dbab7e6380f014为函数eqId4837c94ef0ff4dcf9b1dda4df363275a的极大值点,求证:eqId70009e3bf0234a119bce76e8260fbc8f
3 . 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.
4 . 已知函数eqIde621a57dd8de40688d27c694dca4e61a有两个不同的极值点eqIdca06d7ef3b984e8c8fb8f7d217749d05,则满足条件的eqId70a27b6ddf6b478285353abb3b1f3741取值范围为(   )
A.eqIdf6142709dc8c4193aa4ab2d51353c81bB.eqIddca4c31f92e1447fb6eceb9fdf294175C.eqIdbf051b9dc24e4dd3b863c647130a246eD.eqIdb82139e4836848f79663af8e7848c8a1
5 . 已知函数eqId095ef4a59dde4dada977dc1e6461a2c4
(1)若eqId265cfa2a0c38402ca917f059a6f1565e,讨论eqId4837c94ef0ff4dcf9b1dda4df363275a的单调性;
(2)eqId4837c94ef0ff4dcf9b1dda4df363275a有两个极小值点eqId735b8047beee4dee870fc72ae837a245eqIdecaaaffea9af458c8e6dff16f15c1a73,求实数a的取值范围,并证明eqIda693ccf90b82434a8c970c5acf92f0ee
6 . 已知eqIde9edd995034840cfb557ea415074294aeqId3f7aec534f754627932806daaab3cf96.
(1)当eqId0be4e678c13c4855b0d3f5c45188da09时,求证:对任意eqIdd6464deb126c4f23882fbe0ebecec78deqId2b9c2b69b2e84958ac765ae1e312aa93
(2)若eqId90f4010cc71b4998be6fa90952078f6b是函数eqId6f13759e937144069819aed2ae5a1057的极大值点,求eqId70a27b6ddf6b478285353abb3b1f3741的取值范围.
7 . 函数eqIdc1533ba597c740ce9f4f7437d97071e1的图象在eqId3f4caee77e83440882f7e54ff222babb上恰有两个极大值点,则eqIdb266966a0778497f9ee41fb8dc856b3b的取值范围为(   )
A.eqId691cc4de13c14919871f6816de1a1241B.eqId0ecdcbf3bcd14903bdd6d90fb529dcf6C.eqId619133e203094e869871b523ef2037fbD.eqId25c1d19292c945db8364408eafdfc66a
8 . 已知eqId0990213ca5a3455bb70630faa87b352b.
(1)当eqId0be4e678c13c4855b0d3f5c45188da09时,求函数eqId6f13759e937144069819aed2ae5a1057的导函数eqId67234bd198cf4dd9bf218e2567e2b9c5的最大值;
(2)若eqId6f13759e937144069819aed2ae5a1057有两个极值点,求实数a的取值范围.
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