组卷网>知识点选题>利用基本不等式或柯西不等式求最值
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1 . (1)若ab满足关系eqId0e2db9e1d1da4207a8e8d01c3a6373f0,求eqIdf82588160a0949bfb113971fad9a7f72
(2)设实数xyz满足eqIdd63cf527b7c347e6b936fe0e1a874a27,求eqIdf5b1af7308004dcc96749ac4a80c9b60的最小值.
多选题 | 较易(0.85) | 2021·全国高三专题练习(文)
3 . 下列推导过程,正确的为(   )
A.因为eqId70a27b6ddf6b478285353abb3b1f3741eqIdaea992e70d4943e49e893817eb885ed7为正实数,所以eqIdff2c6d2566364f82a73f0c4880f36f12
B.因为eqId6fc94f6e181444c6b809fb393eb8fae6,所以eqIdd5eac44dbcc94c38acd3222f3eb6886d
C.eqId41f04097a07d4d03941921a18fc42004,所以eqId6e57fd46385542fb964de0246d354d71
D.因为eqIda9cd3f94eb8045438f75e9daccfa7200eqIda96c35333bce498fac43d585fdcaf8c2eqId7c686059c20f45e1bf37750cb72d52f8,所以eqId45faaa3465464592aaa45b5a0da8a445
更新:2021/09/22组卷:138
4 . 已知函数eqId32a3ac2b04884af0b2cddf107046d5b5.
(1)求不等式eqId3f98b30cbd504de3818521f0f1660230的解集;
(2)若正数eqId70a27b6ddf6b478285353abb3b1f3741eqIdaea992e70d4943e49e893817eb885ed7eqId44925af6fb19413689ba5616e3647cba满足eqIdccc2fecbec7643498560898c08910aa8,求eqIdd07f67cef8f7411dab30fda9b2879491的最小值.
解答题 | 一般(0.65) | 2021·河北邢台·
7 . 一个圆心为eqId2efda802d5534f6d92d9f8af7aaec28b的半圆形如图所示,eqId19a4eb16029e4550a14f2afe4741a3c3eqId312ef2c826304089b9b0f1d1e88b0f50在半圆弧eqId99a3187c2b8f4bcc9703c74c3b72f1f3上,eqId83e84aa8089a4e45abdfe2d59f6704abeqId8a76bbe21fb549e3a9c2038d58c7a3d8eqId0627be51821d4be7b3e024a354815d64交于点eqIdbedf755e0fdb4d078d6859360706b163,且eqIdbe18c3a0f5e84065a2876160cb606609.
说明: figure
(1)设eqId264eda0150bd4044948850f17441b6bbeqIdf04ff4b1261a48ffa1788f6f9efa25e9,求eqId072d7d6b911b42bc89207e72515ebf5f关于eqIda9cd3f94eb8045438f75e9daccfa7200的函数关系式;
(2)求eqId88554153853e4e1d862e86a0d3db8057面积的最大值:
9 . 如图,已知圆台高为5,上底面eqId7749df1ac7bf4efb8aa86872dab999bb半径为3,下底面eqId9344dc1195614f22b15a1497450c38c1半径为4,△ABCeqId9344dc1195614f22b15a1497450c38c1的内接三角形,且ABACPeqId7749df1ac7bf4efb8aa86872dab999bb上一点,则PA2+PB2+PC2的最小值为______
说明: figure
单选题 | 较难(0.4) | 2022·上海高三专题练习
10 . 设函数eqIdd1e17f9c856a47a48c890a539dbfa05d,则下列错误的是(   )
A.方程eqIda91fef9877ca4830bc03c3a31eafdd1d有解
B.方程eqIdb46458272f754412b00edcddc5ac7b23 在eqId8f7a462567c24337a20b8016a9d21735 内解的个数为偶数
C.eqId6f13759e937144069819aed2ae5a1057的图像有对称轴
D.eqId6f13759e937144069819aed2ae5a1057的图像有对称中心