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【习题分享】高中数学利用函数最值证明不等式专题

当前时间： 2026-08-10 21:16:05 分类：办公文件 评论(0)
【习题分享】高中数学利用函数最值证明不等式专题

利用函数最值证明不等式

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在近几年的高考和模考中, 出现了不少证明不等式的问题,旨在加大导数运用的推理论证力度.证明不等式最典型的题型便是利用导数研究函数单调性，进而求出最值，利用最值证明不等式成立。以下介绍几种常规题型。

题型一 利用最值直接证明

SPRING

 2025

题型二 作差构造

SPRING

 2025

题型三 适当放缩

SPRING

 2025

PART.THREE

题型四 凹凸反转

SPRING

 2025

END

 裴老师 |15376312928

 李老师 | 15506336636

 孙老师 |17663367194

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  144. /yingpanguazai/ssd/ssd1/www/wwww.yeyulingfeng.com/runtime/temp/c935550e3e8a3a4c27dd94e439343fdf.php ( 31.50 KB )
  145. /yingpanguazai/ssd/ssd1/www/wwww.yeyulingfeng.com/vendor/topthink/think-trace/src/Html.php ( 4.42 KB )
  1. CONNECT:[ UseTime:0.001185s ] mysql:host=127.0.0.1;port=3306;dbname=wenku;charset=utf8mb4
  2. SHOW FULL COLUMNS FROM `fenlei` [ RunTime:0.001856s ]
  3. SELECT * FROM `fenlei` WHERE `fid` = 0 [ RunTime:0.000755s ]
  4. SELECT * FROM `fenlei` WHERE `fid` = 63 [ RunTime:0.000244s ]
  5. SHOW FULL COLUMNS FROM `set` [ RunTime:0.000497s ]
  6. SELECT * FROM `set` [ RunTime:0.000201s ]
  7. SHOW FULL COLUMNS FROM `article` [ RunTime:0.000537s ]
  8. SELECT * FROM `article` WHERE `id` = 921401 LIMIT 1 [ RunTime:0.000446s ]
  9. UPDATE `article` SET `lasttime` = 1786382063 WHERE `id` = 921401 [ RunTime:0.003788s ]
  10. SELECT * FROM `fenlei` WHERE `id` = 64 LIMIT 1 [ RunTime:0.000231s ]
  11. SELECT * FROM `article` WHERE `id` < 921401 ORDER BY `id` DESC LIMIT 1 [ RunTime:0.000433s ]
  12. SELECT * FROM `article` WHERE `id` > 921401 ORDER BY `id` ASC LIMIT 1 [ RunTime:0.000402s ]
  13. SELECT * FROM `article` WHERE `id` < 921401 ORDER BY `id` DESC LIMIT 10 [ RunTime:0.000777s ]
  14. SELECT * FROM `article` WHERE `id` < 921401 ORDER BY `id` DESC LIMIT 10,10 [ RunTime:0.001409s ]
  15. SELECT * FROM `article` WHERE `id` < 921401 ORDER BY `id` DESC LIMIT 20,10 [ RunTime:0.000659s ]
0.196207s