名校
1 . 已知函数
且
.
(1)讨论
的单调性;
(2)若
,求证:
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed08d7cab361dfb5d85bea5844323bf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37fa1476cf3552b9ae91ef039b1c6c80.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5940cc292609708a6491891078fb75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6422b9c2e93a91fe9e39ce4d9dabb0fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/508da79aaa240d1846940c239adb1d62.png)
您最近一年使用:0次
名校
解题方法
2 . 已知函数
.
(1)若
,求实数
的取值范围;
(2)若
有2个不同的零点
(
),求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7a0cce5bbef7a460b6f747c5fb878e7.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2aeda5c6f101566159dd4c460b943b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02cc6315c3dc912dad7a4b5cbca676f0.png)
您最近一年使用:0次
2023-03-04更新
|
2677次组卷
|
7卷引用:山西省省际名校2023届高三联考一(启航卷)数学试题
山西省省际名校2023届高三联考一(启航卷)数学试题(已下线)专题22极值点偏移问题(已下线)拓展九:利用导数研究函数的零点的4种考法总结(1)(已下线)重难点突破05 极值点偏移问题与拐点偏移问题(七大题型)-2(已下线)专题2-6 导数大题证明不等式归类-3吉林省长春市第二中学2024届高三第六次调研测试数学试题(已下线)专题6 导数与零点偏移【讲】
解题方法
3 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4739c39d58db0da5935f1d8468694558.png)
在点
处的切线方程为
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/607c26737551c88b70281a00b1a6ef55.png)
(1)求
的值域;
(2)若
,且
,
,证明:①
;②
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4739c39d58db0da5935f1d8468694558.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88542cb1f25561fa09564eb2e60561a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bea9227dd0104da58e0c40952cc87ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1207a97785e93f1b7ebb7796bc5874d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/607c26737551c88b70281a00b1a6ef55.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba205979166f8fc4f1753d21de7a2af0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a46e678bf9d2df5ad4c782b3dc22f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcf7adcc976209d4b686156120bea276.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b53e2dd26458eb01d97d912ef10ef35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39a38efe32b0f0306f1dd1158ac2bd6e.png)
您最近一年使用:0次
2023-04-21更新
|
935次组卷
|
4卷引用:山西省太原市、大同市2023届高三二模数学试题
山西省太原市、大同市2023届高三二模数学试题山西省阳泉市2023届高三二模数学试题(已下线)押新高考第22题 导数综合解答题(已下线)第二章 函数的概念与性质 第二节 函数的单调性与最值(B素养提升卷)
4 . 已知函数
.
(1)当
时,讨论
的单调性;
(2)若
,当
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/594121dccd132101b030b3dee00f5069.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/859458471c86ae39e0cc42d2d960d03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58d527d2746b7a94fa6e7fbff58619f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a226de479a39a2bc730c2cdbc50850c2.png)
您最近一年使用:0次
2023-05-13更新
|
479次组卷
|
2卷引用:山西省名校联盟2023届高三5月仿真模拟数学试题
名校
5 . 已知
.
(1)若
的图象在x=0处的切线过点
,求a的值;
(2)若
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb41095564f76e3f481f3724e2e3a95e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33cc0f9aa168e43cc5759f017d69b498.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/293d639e67df2da17966a567db2656e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d34808b27aff0403e0cf52aefc25e0.png)
您最近一年使用:0次
2022-04-24更新
|
597次组卷
|
5卷引用:山西省2022届高三第二次模拟数学(理)试题
名校
解题方法
6 . 已知函数
.
(1)判断函数
在
上的单调性;
(2)若
,求证:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/147796e9f9dd9b2db3ee34c77bead238.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a3cee5e50ee4f1dfbcf0ff0312fef1b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9880e3e732466f7cf8daa9eeac6b1c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e01b6fb6a1c7a895df528382a5583444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/997b1519e80741627b21f673f1f4d079.png)
您最近一年使用:0次
2020-03-04更新
|
890次组卷
|
6卷引用:2020届山西省大同市高三模拟数学(文)试题
2020届山西省大同市高三模拟数学(文)试题2020届河南省顶级名校高三1月教学质量测评文科数学试题2020届河南省南阳市第一中学高三第九次数学(文)试题2020届安徽省合肥市高三下学期“停课不停学”线上考试数学(文)试题华大新高考联盟2020届高三1月教学质量测评数学(文)试题(已下线)第42讲 三角函数之放缩法-突破2022年新高考数学导数压轴解答题精选精练
解题方法
7 . 已知函数
,
.
(1)讨论函数
的单调性;
(2)当
,时,若对于任意
,都存在
,使得
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c23ccfd55bdb9b359b33456924db82e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac83fc02f84ca0a931dc930108048b29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d701701514d29d22d56e8a35f797d267.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a99851fb4df35dfb2c4efd4a839b901f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f49f4d25c99663e815060bf6dadec559.png)
您最近一年使用:0次
8 . 已知函数
.
(1)求过点
且与曲线
相切的直线方程;
(2)设
,其中a为非零实数,若
有两个极值点
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee1dcc2a471ac89dd3cec62e77f6ff9.png)
(1)求过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a2a5e336b6bcba6354fd366c892dd06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d836280b3e758c30cbd7e8a5b7fbf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9387c3b3079c432e3845c60466fe0921.png)
您最近一年使用:0次
9 . 已知函数
在
上存在两个零点
,且
.
(1)求实数
的取值范围;
(2)若方程
的两根为
,
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38572ad4ef879663d599510d64c4020f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e1c9c97de9198d47306216e9961b80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64263fe2ca48e694c87496d61e63fb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/770cf3716f1e9dc8023a898df7f33783.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/177e54e8deea5da9dc6bc82eb3de0c2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acb64c72748493af1bcb6a5c0944f505.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eaa3741d84a6f87745db1520ec9b12.png)
您最近一年使用:0次