组卷网>知识点选题>利用导数解决双变量问题
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1 . 已知函数eqId34b396551a4e4fa4bd70057534be33b0eqIdbdd3b393daab4d948c0824b53d39376c,若函数eqId4837c94ef0ff4dcf9b1dda4df363275a的图象与函数eqId28c4c21271884dfeac29ce0222782376的图象的一个公共点eqIdbedf755e0fdb4d078d6859360706b163的横坐标为eqId37705e1ef6a84bbdbe88433e75932cdf且两函数图象在点eqIdbedf755e0fdb4d078d6859360706b163处的切线斜率之和为eqId16fc2c4ac7e940cdad49c4a01d735579.
(1)求eqId4959a8a13c0b40f3a3b076626a4b616c的值;
(2)对任意eqId08c4c2b6410343b1be2693ff3298914f,不等式eqId634eb48b1477496ba9669a50a895d1d3恒成立,求实数eqId4d2187284c5d4de29906363f7d21f60f的取值范围.
解答题 | 较难(0.4) | 2022·全国高三专题练习
2 . 已知函数eqId502eb3f543614c84aca766713e0fdc55eqIde9edd995034840cfb557ea415074294a.
(1)当eqId0be4e678c13c4855b0d3f5c45188da09时,求曲线eqId144eff5c0e4649138a21f2b1b6a06907在点eqIdb58abca134e44fae8038715b1e714449处的切线方程;
(2)若eqId900a1971159149318c4b13c25efe3cb9eqIdf3f3b3f911d948908cb75d8d4627324c,求证:eqIdbf60efa3b86b4d969b91e6f3cff209c5.
更新:2021/08/01组卷:14
3 . 已知函数eqIdc843d5a8b7994d9ba3fd21f70d254c94eqIdca4ab76061b14cdfbb5b2cb8cf37b9c0)有两个极值点为eqId735b8047beee4dee870fc72ae837a245eqIdecaaaffea9af458c8e6dff16f15c1a73eqId69154b0cb5e843698c5ea5bf0d8bdfa8).
(1)求实数eqId70a27b6ddf6b478285353abb3b1f3741的取值范围;
(2)求证:eqId218cfee78ec547abae5e85dfa6ea2816
4 . 已知函数eqId690db8e8ea5f4279b6862dbfce120f47.
(1)求函数eqId6f13759e937144069819aed2ae5a1057在定义域内的最值.
(2)当eqId982da3835b7946d999cc8604a2ece266时,若eqId144eff5c0e4649138a21f2b1b6a06907有两个不同的零点eqId735b8047beee4dee870fc72ae837a245eqIdecaaaffea9af458c8e6dff16f15c1a73,求证:eqId89f46898bcb844d99682f74f4d7120e9.
5 . 已知函数eqIdeb2917fb979d40eb81bc6af71b3c963b,若正实数eqIdca06d7ef3b984e8c8fb8f7d217749d05满足eqId6a0c960e94e74354912f3fa85071c34a,则下列说法正确的是(   )
A.在函数eqId4837c94ef0ff4dcf9b1dda4df363275a上存在点eqId2445f1800d3f4628b7bfe1ec0db9e273,使得函数eqId4837c94ef0ff4dcf9b1dda4df363275a过该点的切线与eqId4837c94ef0ff4dcf9b1dda4df363275a只有一个交点
B.过点eqId769253c23014435e8a96b6bd66657930可作两条切线与函数eqId4837c94ef0ff4dcf9b1dda4df363275a相切
C.eqId5ef4a786ec0e4d33bc9104a888e6de34
D.eqId0c1610c3e7d4444f81948a7e32bfd478的值与2的关系不确定
6 . 已知eqIdd5b4c5b3fa9a4cce9a1427d3a150f328.
(1)若eqIdd78df7c3aa4747a4b868757aa0e4e3f5,求eqId6f13759e937144069819aed2ae5a1057的单调区间;
(2)已知函数eqId6f13759e937144069819aed2ae5a1057有两个极值点eqId703a5624b36649aface380e7b56e4b6ceqId69154b0cb5e843698c5ea5bf0d8bdfa8),若eqIddf365fea33534a45a194addfad04fb22恒成立,试求eqIda4be99d332154d13a4a6ed1ff6444fe7的取值范围.
7 . 已知函数eqId6ba4e4e6aeb247168e0429d77a0782ffeqIdca4ab76061b14cdfbb5b2cb8cf37b9c0).
(1)当eqIdad700a44eaf843cc9443c434a0d01cb0时,讨论函数eqId4837c94ef0ff4dcf9b1dda4df363275a的单调性;
(2)若函数eqId4837c94ef0ff4dcf9b1dda4df363275a恰有两个极值点eqId735b8047beee4dee870fc72ae837a245eqIdecaaaffea9af458c8e6dff16f15c1a73eqId69154b0cb5e843698c5ea5bf0d8bdfa8),且eqId7796b478832f4a2fa873d1d2827aeac3,求eqIdaa967727452442e29e18c734b69bd273的最大值.
8 . 已知函数eqId3290e2c437114d818de0a6c9de955d82有两个不同的极值点eqIdca06d7ef3b984e8c8fb8f7d217749d05
(1) 求函数f(x)的单调区间;
(2) 若eqIde5b00f5ac1c84d378fddfd6178c76d27,使eqIdf8c7dad596d04c08b25e0b28756fa501成立,求实数t的取值范围.
9 . 已知函数eqIdf48656c03c90497cb30520862d2afec0有两个零点eqId735b8047beee4dee870fc72ae837a245eqId206ae65979ff47e0a2f1c9c59bd20d91.
(1)求实数eqId70a27b6ddf6b478285353abb3b1f3741的取值范围;
(2)证明:eqId37fcc06421f74c54a26f96771572535d.
10 . 已知函数eqIde071975ff4574e7ebee6099c498bc4fc.
(1)当eqIdad700a44eaf843cc9443c434a0d01cb0时,讨论函数eqId6f13759e937144069819aed2ae5a1057的单调性:
(2)若函数eqId6f13759e937144069819aed2ae5a1057恰有两个极值点eqId201fa446b9c440e3983d104b24e1f717,且eqId062484d1173c4b4d9a17e5a573112853,求eqIdaa967727452442e29e18c734b69bd273的最大值.
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