组卷网>知识点选题>分类讨论法解决二次函数闭区间上的最值问题
显示知识点
显示答案
| 共计 476 道试题
3 . 设向量eqIdf20fe6ba370248c8b79dd03cc7549d9beqId3eb5e37b28034683b3e97aa76da7196dxeqIda96c35333bce498fac43d585fdcaf8c2),满足eqIdc920ebf1b4114dff930b8f5e4c785666
(1)求点eqId035bf781173e4f769ee7951a91ad216b的轨迹c的方程;
(2)设eqIde24d2bf27580450993131d9f4dfb04b9eqId982da3835b7946d999cc8604a2ece266),P为曲线C上任意一点,求A到点P距离的最大值eqId707f29157f9646f9a70e798bd5963c9a
4 . 某开发商拟开发新建一批商业用的门面房,开发商对有意在该地段购买门面房的购房人进行随机调查得到每套门面房的销售单价eqIda9cd3f94eb8045438f75e9daccfa7200(单位:百万元)和销售量eqId072d7d6b911b42bc89207e72515ebf5f(单位:套)之间的一组数据,如下表所示:
每套销售单价eqIda9cd3f94eb8045438f75e9daccfa7200/百万元
eqId16fc2c4ac7e940cdad49c4a01d735579
eqId87cd90ad3d544be7b4d9d3fb15dc68ab
eqId62503849440740cf8754af7e844ba72c
eqId57b1e5088b9448a78fbaa091fa42a986
eqId45cfebd3a8e54d27aa04ffed2e4eb0b6
销售量eqId072d7d6b911b42bc89207e72515ebf5f/套
eqId45cfebd3a8e54d27aa04ffed2e4eb0b6
eqId45cfebd3a8e54d27aa04ffed2e4eb0b6
eqId62503849440740cf8754af7e844ba72c
eqId16fc2c4ac7e940cdad49c4a01d735579
eqId401586f7a7f248b7904a4cfeaa2ed2f0
(1)试根据表中数据,建立eqId072d7d6b911b42bc89207e72515ebf5f关于eqIda9cd3f94eb8045438f75e9daccfa7200的回归直线方程;
(2)从反馈的信息看购房人对该门面房的心理价位在eqId191bd36491b9409498e828464e3aa6f8(单位:百万元/套)内,已知该门面房的成本是eqId70a27b6ddf6b478285353abb3b1f3741百万元/套eqId32509fe2cfa04c9e87c12dab10fe80a7,试探究每套门面房销售单价定为多少时,开发商才能获得最大的利润?(注:利润=销售收入-成本)
附:线性回归方程eqIdd1251868f5af4d44b51b8a50ace7eb65的系数公式eqId8d7673618e614ab6bedfafa830bc26a3eqId4b0bdc60709b48aebf4c56c9c5e32482.
5 . 已知函数eqIddca6bad54ac74916a5567f8847597601eqIda4be99d332154d13a4a6ed1ff6444fe7为常数)
(1)若函数eqId144eff5c0e4649138a21f2b1b6a06907图象上动点P到定点Q(0,2)的距离的最小值为eqId3385c7d74629435abd34488e4cc89b4c,求实数eqIda4be99d332154d13a4a6ed1ff6444fe7的值;
(2)设eqId16d341aeb9954b6da88ebdf00b951972,若不等式eqId548578ce43dd4a0ab2a7b5b70f9f1ee4eqIdb6df6cfc32614394a263bfc8111a1290有解,求eqId4d2187284c5d4de29906363f7d21f60f的取值范围;
(3)定义:区间eqId0005bc5d2f554698afeb8f199bc0cd81eqId5bddd85585e34be18dfbae00574217d8)的长度为eqIdd3e739f7f69d4432a1cf3eb7fe0548e9,若eqId51b8de66b30c4539b899dc2a7b0c5aa4,问是否存在区间eqId0005bc5d2f554698afeb8f199bc0cd81,使得eqId6f13759e937144069819aed2ae5a1057的值域为[6,7],若存在,求出此区间长度的最大值与最小值的差.
6 . 已知函数eqId66c3f02a02994279a58822dda506bd93的定义域为eqIda66fbc65e8634e799cf8f434e9b0252d,在该定义域内函数的最大值与最小值之和为eqId1d18010fc29e4f45abaaece953793246,则实数eqId69f56ef2c88b4b73a560da59f5247a82可取(   )
A.1B.2C.3D.4
7 . 已知函数eqId2534159516d54e1593e7ecf02fee0b6c,若对于任意的eqId735b8047beee4dee870fc72ae837a245eqIdecaaaffea9af458c8e6dff16f15c1a73,且有eqId489aa8ef10e3467aac535d61074914b3,均满足eqId3de6ebd5b1e14cc98fbd4f057b64f376
(1)求a的取值范围?
(2)当eqIdd8968ea87af34c0fa7aa66a821c42301,函数eqId6f13759e937144069819aed2ae5a1057的最小值为Ma),对于给定范围内的实数a,求得Ma)的最小值.
8 . 已知二次函数eqIdd97ac3da3cd74a508bd009a0d8f5954d.
(1)若eqId6f13759e937144069819aed2ae5a1057是偶函数,求m的值;
(2)函数在区间eqIdd5962c71196d40b28b2ca0d7b748b66d上的最小值记为eqId69e01450ca4b4cb0815e18d10ebcb297,求eqId69e01450ca4b4cb0815e18d10ebcb297的最大值;
(3)若函数eqId48a08162af814cfdb0e426afbfae7551eqIdf173839cbdf549429066610d1a327f06上是单调增函数,求实数m的取值范围.
9 . 在平面直角坐标系中,eqId2efda802d5534f6d92d9f8af7aaec28b为坐标原点eqId646385a87fdc4af7b146ba3a461e6ed1,若存在实数xy使得eqId9cfb168ae72a49138b6a8cb1ac3fce7a,且eqIda6002ac978ce41fbb28e656514038cc9
(1)求函数关系式eqId144eff5c0e4649138a21f2b1b6a06907
(2)已知的数eqId144eff5c0e4649138a21f2b1b6a06907的定义城为[1,4],若函数eqId23b15575906b41c898118a88a374935a的最小值为eqId3b29afc35d5a4bdfab8a0674ec37b12d,求实数m的值.
10 . 已知函数eqIdc21524908e1c430a9f24dde3886ff6afeqId82ade16d79cc490384d3aa5994a54958
(1)当eqId00ca497c1da94424a68ba665cb53b82d时,求eqId6f13759e937144069819aed2ae5a1057的最小值;
(2)若eqId144eff5c0e4649138a21f2b1b6a06907在区间eqIda433f1a66bfc4453803c35a0ed5a5296上的最大值为14,求实数eqId70a27b6ddf6b478285353abb3b1f3741的值.