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1 . 已知函数eqId3d693ac841e54a19889f2e230fc7d330eqId400b8c2754494564baefd34518bcb6c6.
(1)当eqIdd78df7c3aa4747a4b868757aa0e4e3f5时,求曲线eqId144eff5c0e4649138a21f2b1b6a06907eqId4f5eb7fe34bf4315924b7d83c40e99d3处的切线方程;
(2)求函数eqId6f13759e937144069819aed2ae5a1057的单调区间;
(3)当eqId982da3835b7946d999cc8604a2ece266时,求函数eqId6f13759e937144069819aed2ae5a1057的最大值.
2 . 已知曲线eqIdcf24ec73ec434fd8a993f40101844b2c.求该曲线的过点eqId9c079586fb8c46d89c260aef3a484e15的切线方程.
4 . 已知函数eqIda568f5125c234ec68c7b31662946503ceqIde9edd995034840cfb557ea415074294a
(1)当eqId0be4e678c13c4855b0d3f5c45188da09时,求曲线eqId10852d81bc184140a7780250c82c6929在点eqId2cb0b5c25a7e411abb9bf0c694c7c4ac处的切线方程;
(2)若eqId10852d81bc184140a7780250c82c6929在区间eqId787fec3796eb4e9983c24c49d247da44上有唯一的极值点eqId761b2917a82b4524b8dbab7e6380f014,证明:eqId40b58e26e2aa4e59a117089253337634
5 . 已知函数eqId3f12f121055f43748f346d19a330eb9feqId8f941ae1b47d41ff956e6541ede690ca,直线eqId417e80f1349244878d01fe90e0891f5feqId10852d81bc184140a7780250c82c6929的图象相切于点eqIddf6ff38451f04add900431590850c424,若直线eqId417e80f1349244878d01fe90e0891f5feqId28c4c21271884dfeac29ce0222782376的图象也相切,则eqId783c5f01aa1e49b29f88c27d2eca4354(   )
A.eqIda86879ae304449a4a6e6461c485a1f13B.eqIdbeffaaf8d5cd43cf8375210d69fce6beC.eqId8898c1dc81824f3098bbeae74e8f11fdD.eqIdbeffaaf8d5cd43cf8375210d69fce6beeqId8898c1dc81824f3098bbeae74e8f11fd
6 . 已知函数eqId7159ee07ed9e46139fc751e040daf54ceqIdca4ab76061b14cdfbb5b2cb8cf37b9c0
(1)当eqId0be4e678c13c4855b0d3f5c45188da09时,求曲线eqId10852d81bc184140a7780250c82c6929在点eqId2cb0b5c25a7e411abb9bf0c694c7c4ac处的切线方程;
(2)若eqId10852d81bc184140a7780250c82c6929在区间eqIda4e2c966d65d40b5b82aaaa6f0af4cb9上有唯一的极值点eqId761b2917a82b4524b8dbab7e6380f014,求eqId70a27b6ddf6b478285353abb3b1f3741的取值范围,并证明:eqIdeaddd1318d514da4b2904ae8767ba164
7 . 已知函数eqId5f1d8d847ef2424aa11aaf9fb8b4f578eqId6d1f986666e741d1994f91d65530ee49.
(1)若函数eqId10852d81bc184140a7780250c82c6929eqId28c4c21271884dfeac29ce0222782376x=1处的切线平行,求函数eqId28c4c21271884dfeac29ce0222782376eqIdfb275f54da47478da25465bce6d5c214处的切线方程;
(2)当eqId7a27098289c64d7aa1708271bb3e2d80时,若eqIdfb0fede0023f441da607760c398cdb46恒成立,求实数a的取值范围.
8 . 已知函数eqId58867685bc2b4f5aa22655f9da4d82a2eqId650cb71e8b144af68ebc49111e8be282eqIdd5a6569623204652aada8c497a766e0a处取得极值.
(1)求实数eqId70a27b6ddf6b478285353abb3b1f3741的值及函数eqIde4a0e3706b56447b90fe1b2781f91b14的图象在点eqIda4b2971e99c44388a50263b79575abcc处的切线的方程;
(2)求函数eqIde4a0e3706b56447b90fe1b2781f91b14的极小值.