组卷网>知识点选题>二次不等式恒成立问题
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解答题 | 一般(0.65) | 2018·义乌市义亭中学高一期中
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1 . 已知函数eqId943a627e918f40b7bb0ec4fc2e6db8dfeqIdb8006756d6d54eb29dec66a77dddfd62
(1)若不等式eqId581752034a1745aa9d7bbba4eefa94a2对任意的实数eqIda9cd3f94eb8045438f75e9daccfa7200恒成立,求实数eqIdaea992e70d4943e49e893817eb885ed7的取值范围;
(2)设eqId736eab91294d481e8dca6c085774560a,且eqId0dc74c9e57e94a16a59d8bccce45c755eqIda75f32d729e345fca573383b8c130842上单调递增,求实数eqIda4be99d332154d13a4a6ed1ff6444fe7的取值范围.
2 . 已知二次函数eqId39c09443f2944681a5719f1ede098af3
(1)若1是eqId6f13759e937144069819aed2ae5a1057的一个零点,求实数eqId4d2187284c5d4de29906363f7d21f60f的值;
(2)若eqId0836c1003605494a89734a73b75e144ceqId6709283711bf4ae39fde99d031d3bb28恒成立,求实数eqId4d2187284c5d4de29906363f7d21f60f的取值范围.
3 . 已知定义域为R的函数eqIde12afc94a8cd4e02ab9a813180da452c是奇函数.
(1)求ab的值;
(2)判断fx)在定义域R上单调性并证明
(3)若对于任意eqId6fc94f6e181444c6b809fb393eb8fae6,不等式eqIdf2c21630cd5443fba7f1adda53e20077恒成立,求k的范围.
4 . 已知函数eqIdf8eb4a6854a448ae9080568d65495973,如果对于定义域eqId0cd8063abf2b458f80091bc51b75a904内的任意实数eqIda9cd3f94eb8045438f75e9daccfa7200,对于给定的非零常数eqIda4be99d332154d13a4a6ed1ff6444fe7,总存在非零常数eqIdf8ef9ec340b848fc8802eec4cf1a8b89,恒有eqId4f85955465b94636b6be36e917605d65成立,则称函数eqId6f13759e937144069819aed2ae5a1057eqId0cd8063abf2b458f80091bc51b75a904上的周期为eqIdf8ef9ec340b848fc8802eec4cf1a8b89eqIda4be99d332154d13a4a6ed1ff6444fe7级类周期函数.
(1)已知eqId144eff5c0e4649138a21f2b1b6a06907eqId1d40c107624b4197bad0d10756051733上的周期为1的eqIda4be99d332154d13a4a6ed1ff6444fe7级类周期函数,且eqId144eff5c0e4649138a21f2b1b6a06907eqId1d40c107624b4197bad0d10756051733上的严格增函数,当eqId2e18f0fd096f4eb7b1014b7e745d6e20时,eqIdc849966698b946dfb67f33df021d9c55,求实数eqIda4be99d332154d13a4a6ed1ff6444fe7的取值范围;
(2)设函数eqId6f13759e937144069819aed2ae5a1057eqId7dcd2312d0bf4bb1befdfcc170e45791上的周期为1的2级类周期图数,且当eqIdd6d95d40fada4104b134946a91ebd2e8时,eqIde97839ca5d054860a91af73509e83d38.若对任意eqId3ffc22adf8fc45dfb573e0030904d00d,都有eqId5bf5bc104e9b4479861703f37593dd29,求eqIda4be99d332154d13a4a6ed1ff6444fe7的取值范围;
(3)是否存在实数eqId4d2187284c5d4de29906363f7d21f60f,使函数eqIdc8cfe64afe1e437fb223d1aa09a0e35ceqId7dcd2312d0bf4bb1befdfcc170e45791上的周期为eqIdf8ef9ec340b848fc8802eec4cf1a8b89eqIdf8ef9ec340b848fc8802eec4cf1a8b89级类周期函数,若存在,求出实数eqId4d2187284c5d4de29906363f7d21f60feqIdf8ef9ec340b848fc8802eec4cf1a8b89的值,若不存在,说明理由.
解答题 | 较易(0.85) | 2021·北京高二期末
5 . 已知函数eqId1d29d30ca25540b6b700ebd3a25a8686eqIdca4ab76061b14cdfbb5b2cb8cf37b9c0.
(1)当eqId316e2199840e418e87252dba1d7d7ffd时,求不等式eqId78589ede94d94669a27c18ab91998333的解集;
(2)若关于eqIda9cd3f94eb8045438f75e9daccfa7200的不等式eqId8b037e9eecfe483d8a6e967600e6c554eqId7d7f4d303aab47e9b67ef37b1da7fb62上恒成立,求eqId70a27b6ddf6b478285353abb3b1f3741的最大值.
6 . 已知二次函数eqId6f13759e937144069819aed2ae5a1057的最小值为1,且eqIda6e7bd7f36ff46d68690253845a1593a
(1)求eqId6f13759e937144069819aed2ae5a1057的解析式;
(2)若eqId6f13759e937144069819aed2ae5a1057在区间eqId842d19f1619049fcb7631579d0063dbb上不单调,求实数a的取值范围;
(3)在区间eqIdce200b76babe4284ae3e60dc50a9001e上,eqId144eff5c0e4649138a21f2b1b6a06907的图象恒在eqIdb03cf6eef1394c27a2f19fa39990d1e5的图象上方,试确定实数m的取值范围.
7 . 已知函数eqId601460550be242ea8a34ae2b4a859f24满足eqId28f5b3230ed84edc922c25ea6c174b1f
(1)求eqId53dadb9f9a73437da8ceebc06b510fd9的值;
(2)求eqId601460550be242ea8a34ae2b4a859f24的解析式;
(3)若eqIdeebdffbe88ef44abb0b999c3902d27b7eqId8ccbf04e8c9a460e9db5e8c1912e08b9恒成立,求eqIda4be99d332154d13a4a6ed1ff6444fe7的取值范围.
8 . 已知eqId89f2e4143de24e1d8f2a135fb32ea7ef.以下四个命题:
①对任意实数eqIda9cd3f94eb8045438f75e9daccfa7200,存在eqId4d2187284c5d4de29906363f7d21f60f,使得eqIdac121730997d49c1b6e9356c505f15d1
②对任意eqId4d2187284c5d4de29906363f7d21f60f,存在实数eqIda9cd3f94eb8045438f75e9daccfa7200,使得eqIdac121730997d49c1b6e9356c505f15d1
③对任意实数eqId4d2187284c5d4de29906363f7d21f60feqIda9cd3f94eb8045438f75e9daccfa7200,均有eqIdac121730997d49c1b6e9356c505f15d1成立;
④对任意实数eqId4d2187284c5d4de29906363f7d21f60feqIda9cd3f94eb8045438f75e9daccfa7200,均有eqId0836c1003605494a89734a73b75e144c成立.
其中所有正确的命题是(   )
A.①②B.②③C.①③D.②④
解答题 | 一般(0.65) |
9 . 已知函数eqIde4f117c4403d40ee81f5d021c16809f0.(其中eqIde9edd995034840cfb557ea415074294a为常数)
(1)当eqIda7f410a04f1e4e71af7c4ba54c47ef1f时,不等式eqId8e9dcf35472040849736c89172f09935恒成立,求实数a的取值范围;
(2)当eqIddba619406f1a4237943c5d20adc71f45时,不等式eqId662b5315a0364c2fb18dc3cb2d4860a5恒成立,求实数a的取值范围.
更新:2021/06/24组卷:1029
解答题 | 一般(0.65) |
10 . 设eqIdc9a1976ae2ea413fa3ddd9af076ff01d,函数eqId3bf6b8d5b6644a7f8190cdb51cfc06cdeqId79b269fa8b4d4c74a758a517d701dbc0,且eqIdd3686fd536054cdc9cb83738743248fc
(1)当eqId316e2199840e418e87252dba1d7d7ffd时,若eqId6f13759e937144069819aed2ae5a1057eqId465d08c865e8408c92cfa3d25850b4f7上是单调递增函数,求b的取值范围;
(2)若eqIdf2d6c51dba414304b7a73eb3bd18cf85R上恰有3个相异实根,求a的值;
(3)设eqId42ca474683924aeda9d93f1d3e174883,若对任意eqId3d84da776643420087d06fbd524a7e97,都有eqIdbc16a1bdd7174896bc38544c2aaf55d2,求eqIdaae2f54c772941c29723b00aff1e2212的最小值.
更新:2021/06/13组卷:223
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