组卷网>知识点选题>利用导数解决恒能成立问题
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1 . 已知函数eqId446dc32036fb4bd7bd1c80e3a1f5af32.
(1)若eqId4837c94ef0ff4dcf9b1dda4df363275a有两个零点,求eqId70a27b6ddf6b478285353abb3b1f3741的取值范围;
(2)设eqId64340559eb3e4fce9fd6788effdf83e4,若对任意的eqIddb2434488713493c848a36c620dcdcaf,都有eqId9bf9493a77e744f292e51c204f4f45ee恒成立,求eqId70a27b6ddf6b478285353abb3b1f3741的取值范围.
解答题 | 较难(0.4) | 2021·江苏南通市·高三其他模拟
2 . 已知函数eqId5a6ae34d4d5541d19ed02ba9457fed5feqIde970b61d712c4fe9a0338974d1875833,其中eqIdf035b8f27d4645bb9f6a66f4a3f51918为自然对数的底数,eqIdca4ab76061b14cdfbb5b2cb8cf37b9c0.
(1)若对任意的eqIdc770001e6d044e4eac81750f07ec6779,总存在eqIde322beb7890947fc9469f73d10536473,使得eqId15067fa5ce474e9da50ee7b6d858a6b4,求eqId70a27b6ddf6b478285353abb3b1f3741的取值范围;
(2)若函数eqId9b37d03e47a347fc8fab9f814ba5fac4的图象始终在函数eqId61eedfe297e74edabc9db63b1c3a6cd4的图象上方,求eqId70a27b6ddf6b478285353abb3b1f3741的取值范围.
3 . 已知函数eqIdb8908dd582024a0fad4777166beb0d96,存在实数eqId98ae904219204dfb85da1328a2ac7b3e,使eqId144eff5c0e4649138a21f2b1b6a06907的图象与eqIde333b4c7d97a41e4adb21a02be58bd57的图象无公共点,则实数b的取值范围为__________
解答题 | 较难(0.4) | 2021·浙江高二期末
4 . 已知函数eqId5ce645d100b842e4a14d570efede0d24的一个极值点是eqIdc5faa3a08c944a41850c52572707bcad
(Ⅰ)当eqId316e2199840e418e87252dba1d7d7ffd时,求b的值,并求eqId6f13759e937144069819aed2ae5a1057的单调增区间;
(Ⅱ)设eqId982da3835b7946d999cc8604a2ece266,若eqId090438c5969146bcb415366235f01f07,使得eqId3bf57b4394c648b1acc0e8bb901ec591成立,求实数a的范围.
更新:2021/06/16组卷:0
5 . 已知曲线eqIdcc900f656d6c4deeb4a5a8b4747bcbec.
(1)当a=1时,求曲线在x=1处的切线方程;
(2)对任意的x∈[1,+∞),都有eqId2b9c2b69b2e84958ac765ae1e312aa93,求实数a的取值范围.
6 . 已知eqId8fbd918a673a482da70ec446d7bed7c1.
(1)若函数f(x)在(0,f(0))处的切线与直线x﹣2y+2=0垂直,求a的值;
(2)若在[﹣1,1]上,f(x)≥﹣1,求a的取值范围.
7 . 已知函数eqId4cf319e64a0c4ecbae15be2398103404,若eqIdb77e1897344e4b11be0acbf315d91a32对任意eqId85eb53575dd34c888bbb489e15f1b57e恒成立,则实数a的取值范围为________
8 . 已知函数eqId5f889442e0fd43bd9178184f5cc4e38f(其中eqId7fd12a1dccdd49bfb46543ccc297ec82…为自然对数的底数).
(1)求证:当eqIda73db392e835415db4f07895049ed729时,eqId5f4ee380d2c941b0b79ef2a7338ed546
(2)若不等式eqIdf5aa7d236090484d922f1331eda84f6feqIdb940e6eb1cb4452eb06eb321b9356056成立,求实数a的值.
填空题 | 一般(0.65) | 2021·全国高二专题练习(理)
9 . 已知eqId94a4fe99a84341cd9a23c88c9a33428e,若对任意两个不等的正实数eqIdc869538a648e43cba7dc10c1fae22d9e都有eqIddb3c8058220544b9971d33d54e79a9d0恒成立,则eqId70a27b6ddf6b478285353abb3b1f3741的取值范围是____________
更新:2021/06/13组卷:0
10 . 已知函数eqId7c596084bed44b7ca5f61bf4053c31d7
(1)讨论eqId6f13759e937144069819aed2ae5a1057的单调性;
(2)当eqIdc9a29ac6eb184857bd8ac4610e096249时,eqId2b9c2b69b2e84958ac765ae1e312aa93恒成立,求eqIda4be99d332154d13a4a6ed1ff6444fe7的取值范围.
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