组卷网>知识点选题>利用导数求解函数的极值
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1 . 已知函数eqId58867685bc2b4f5aa22655f9da4d82a2eqId650cb71e8b144af68ebc49111e8be282eqIdd5a6569623204652aada8c497a766e0a处取得极值.
(1)求实数eqId70a27b6ddf6b478285353abb3b1f3741的值及函数eqIde4a0e3706b56447b90fe1b2781f91b14的图象在点eqIda4b2971e99c44388a50263b79575abcc处的切线的方程;
(2)求函数eqIde4a0e3706b56447b90fe1b2781f91b14的极小值.
多选题 | 较难(0.4) | 2021·全国高二课时练习
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4 . (多选)材料:函数是描述客观世界中变量关系和规律的最为基本的数学语言和工具,初等函数是由常数和基本初等函数经过有限次的有理运算及有限次的复合所产生的,且能用一个解析式表示的函数,如函数eqId01b5ee9f609b41ccbf485712ab85898eeqIdaa1312dcc8e24925b421f7767761a363),我们可以作变形:eqId6bd55ede7491473f97d4a1e17dde3cfd,所以eqId01b5ee9f609b41ccbf485712ab85898e可看作是由函数eqId3f6b652d34ea4f938a622755f6cc8657eqId7ea6c212c87d44268974b4787d7cef9b复合而成的,即eqId01b5ee9f609b41ccbf485712ab85898eeqIdaa1312dcc8e24925b421f7767761a363)为初等函数.根据以上材料,对于初等函数eqId475a68f07a4142c0a64a7cd4c1692072eqIdaa1312dcc8e24925b421f7767761a363)的说法正确的是(   )
A.无极小值B.有极小值1C.无极大值D.有极大值eqId048a9bdef2b843cfad04bc99b5b549c6
解答题 | 一般(0.65) | 2021·全国高二课时练习
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5 . 求下列函数的极值:
(1)eqIdd6011761e13b410aa5cdd2706b1c496b
(2)eqId42a3c99d7fe44a3c840179b0c766f491
6 . 已知eqIdd26cd9f8ad374ae192a20aada45c1618为函数eqId10852d81bc184140a7780250c82c6929的导函数,若eqIdecaa6f7c29f1465e86446ff15202d720eqId3304bda99eea43b29124204e06cf1233,则下列结论正确的是(   )
A.eqIdd05fc5c6e8f8437881e4a9fb57fe5170eqIddca4c31f92e1447fb6eceb9fdf294175上单调递增
B.eqIdd05fc5c6e8f8437881e4a9fb57fe5170eqId787fec3796eb4e9983c24c49d247da44上单调递减
C.eqIdd05fc5c6e8f8437881e4a9fb57fe5170eqIddca4c31f92e1447fb6eceb9fdf294175上有极大值eqId49b7b111d23b44a9990c2312dc3b7ed9
D.eqIdd05fc5c6e8f8437881e4a9fb57fe5170eqIddca4c31f92e1447fb6eceb9fdf294175上有极小值eqId49b7b111d23b44a9990c2312dc3b7ed9
7 . 已知函数eqId15046b61ed6d4f98a8666beb736d9525
(1)求函数eqId10852d81bc184140a7780250c82c6929的极值;
(2)设函数eqIdd05fc5c6e8f8437881e4a9fb57fe5170,若存在区间eqId69e27f5587524fec9cb20778ca4f8b49,使得函数eqId28c4c21271884dfeac29ce0222782376eqId0ce7d6f52ab145b7b1ac946de1aada81上的值域为eqIdd17ac14ef9ec42488af9a8db372f43fb,求实数k的最大值.
9 . 已知函数eqIdfab9f54a35e540e9bacaa4905627d940eqIde9edd995034840cfb557ea415074294a.
(1)当eqId37303db52eae469a99849374b5331b25时,直线eqId417e80f1349244878d01fe90e0891f5feqId9b37d03e47a347fc8fab9f814ba5fac4相切于点eqId789888a3c2a64c249743b14cd7ef4c79,求eqId10852d81bc184140a7780250c82c6929的极值,并写出直线eqId417e80f1349244878d01fe90e0891f5f的方程;
(2)若函数eqId9cce2647ff244c00b93b58dd1e578e7c有且只有两个不同的零点eqId735b8047beee4dee870fc72ae837a245eqIdecaaaffea9af458c8e6dff16f15c1a73,求证:eqId81adb08f138b48129cf6868716b55c2f.
10 . 已知函数eqIdea5921bbfdfb493389eae7aea5f34c08
(1)试求函数eqId10852d81bc184140a7780250c82c6929的极大值与极小值;
(2)若曲线eqId9b37d03e47a347fc8fab9f814ba5fac4上存在两个不同的点AeqId8754ce8cf7f34f04abb9a0c041f57f5c,在AeqId8754ce8cf7f34f04abb9a0c041f57f5c处的两条切线都与eqId072d7d6b911b42bc89207e72515ebf5f轴垂直,且线段eqId99a3187c2b8f4bcc9703c74c3b72f1f3eqIda9cd3f94eb8045438f75e9daccfa7200轴相交,求实数eqId70a27b6ddf6b478285353abb3b1f3741的取值范围.