组卷网>知识点选题>定义法判断证明函数的单调性
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1 . 已知函数eqIdc6bc2ee2d8e84c5f877967dd53740228,且eqId9bd4056b478b4ecfaf5cb00267644b31.
(1)证明eqId4837c94ef0ff4dcf9b1dda4df363275aeqIddca4c31f92e1447fb6eceb9fdf294175上单调递增;
(2)若不等式eqId9ecd0fbd8adc48dbb680fcb4aba7810feqIdde46290baec04ea1a59331d8d94f28df上恒成立,求实数eqId70a27b6ddf6b478285353abb3b1f3741的取值范围.
2 . 已知函数eqId0e6ddbb0203244db880e2952db85afa3
(1)用定义法证明:eqId4837c94ef0ff4dcf9b1dda4df363275aeqIddc238b11429b452d82c01b0235c4cadc上单调;
(2)求eqId4837c94ef0ff4dcf9b1dda4df363275aeqIddc238b11429b452d82c01b0235c4cadc上的最大值与最小值.
3 . 用定义证明eqId4c1bbe4a53554a999918eae14f365c9ceqIdd24d16adf82749f2bba9ed400bbc91a6上单调递增.
4 . 已知函数eqIdde9ad9fdbbc741668f6e2d4fecb82307 ,且eqIdc2a7f3e6021d4197b111553fe9c9cfc4 .
(1)求实数eqId70a27b6ddf6b478285353abb3b1f3741的值;
(2)判断函数eqId4837c94ef0ff4dcf9b1dda4df363275aeqId9ff3c9aa7a4a4b9397a6fe8a585a6983上的单调性,并用定义证明;
(3)求函数eqId4837c94ef0ff4dcf9b1dda4df363275aeqIddc07b7fe3c1543ca99a50973d5838649上的最值.
6 . 下列说法不正确的是(   )
A.集合eqIdd88af72f19194a72b490b485675a589a的真子集个数为eqIdaac3aff10a1e4453ba35a55a48eeebb4
B.“函数eqIdf877520c6b25428da7a820cc70dc978e恒成立”是“eqId50e154a2496f4314a1ea191b726c2d65”必要条件
C.已知eqId6ebe0825071a4cc2ad1c1376e1106c77,则函数eqId4837c94ef0ff4dcf9b1dda4df363275a在定义域上单调递增
D.函数eqId833f98e36e9943ca8f9b8ff4764b7a31的最小正周期为eqIdf1470514d3384b7d8224a7712ab506bd
7 . 已知函数eqId19b93b8f34dc42209c2543e66a99e730是定义在R上的奇函数,且eqId5d514c5cdaf14474ad18b03466bc99ad
(1)求f(x)的解析式;
(2)若存在eqId895568b9072440b98cda9d431a866a31,使得eqId803ad9205ae049519a95d8b91e3776ae成立,求m的取值范围.
8 . (1)已知eqId18513915a070416db1e6b2d279419695,且eqId1a5799a97cc746bbb6cd6693f6cc55e9,用分析法证明:eqId92dfeaac862d4278bebd16d8b08392e4
(2)已知函数eqId0f79b3ad18e14570912aebc658998e17,证明:eqIde4a0e3706b56447b90fe1b2781f91b14eqId176a569ddabd4e4482d9ab5af6e2d6ea上单调递增.
9 . 已知函数eqId9b37d03e47a347fc8fab9f814ba5fac4的定义域为eqIddca4c31f92e1447fb6eceb9fdf294175,且满足eqId95cba1af0e0748ebb69769f185122cee,当eqIdda6dbf4054714e318eb596a5a0d1789b时,有eqId78589ede94d94669a27c18ab91998333
(1)判断并证明函数eqId9b37d03e47a347fc8fab9f814ba5fac4的单调性;
(2)对任意eqIdcc23c4100da8408198bef66a957334f3恒成立,求实数eqId70a27b6ddf6b478285353abb3b1f3741的取值范围.
10 . 已知函数eqIdc8f980347a884b918af6e2fc39ebe7cbR上的奇函数.
(1)求eqId70a27b6ddf6b478285353abb3b1f3741的值;
(2)用定义证明eqId6f13759e937144069819aed2ae5a1057eqId7dcd2312d0bf4bb1befdfcc170e45791上为减函数;
(3)若对于任意eqId4bee9fb57138460e96fc45cab45ce18e,不等式eqId30cec72853064561bf4b599d2d32b5e2恒成立,求实数eqId4d2187284c5d4de29906363f7d21f60f的取值范围.
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