已知函数
,其中
.
(1)若
,
,求
的对称中心;
(2)若
,函数
图象向右平移
个单位,得到函数
的图象,
是
的一个零点,若函数
在
(
,
且
)上恰好有8个零点,求
的最小值;
(3)已知函数
,在第(2)问条件下,若对任意为
,存在
,使得
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dc83360ee915013086a987281278639.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4456675a5dbe545462a22cef9aca8fe.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deb73539af255bde55d682b0d0ca735f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa9ceace94f41fcf47aa3ba6ca444a6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83f95e85ce6707ff4161cc675665c557.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9895bf4192f5c55c16f8270d53c49b13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8440725e1df5ca0990b572dd84127914.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb7961cbe98aac6a5fdee94582c341b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64da75a02173c2a5eb40f4c68d0f4f36.png)
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b0d3f5247aced48d54b594ec3522628.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e538686939002a2ba06670615144c73d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83caece05b586ec9e2d6f1ec69449550.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b56a0bc723618e7cdac994882c807bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
更新时间:2024-05-27 22:24:49
|
相似题推荐
解答题-问答题
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较难
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【推荐1】已知函数
,
(1)当
时,求
在区间
上的最大值(用含b的式子表示);
(2)如果方程
有三个不相等的实数解
,
,
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2f5f77306cf4cddf84d040059af0880.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b841ee9ee65c7f0e4e9a5cdeaf47330b.png)
(2)如果方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b92b70365c63607daecdc8deb73ecf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52079d948ae0e1f1d112b3ac76142f1a.png)
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【推荐2】已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eeb55709b7763d692f9433e01a1db47.png)
.
(1)当
时,求
在
上的最值;
(2)设
,若
有两个零点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eeb55709b7763d692f9433e01a1db47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c235ca725ade5c8b07943ac106a90fb3.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ead3fdcb8fe8f5eb3dbe7d96cabc28b.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47417cb76ffb1e8e2538367c123b612c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa662f0273f0921c1fa4727f632395.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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【推荐3】定义一种新的运算“
”:
,都有
.
(1)对于任意实数a,b,c,试判断
与
的大小关系;
(2)若关于x的不等式
的解集中的整数恰有3个,求实数a的取值范围;
(3)已知函数
,
,若对任意的
,总存在
,使得
,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c3c2f679d53b91088ba6eb14c16cbc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2671f593186fa00f17ad26eba7b8f3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a8c23336002eb5d7c478479fcda799f.png)
(1)对于任意实数a,b,c,试判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fda9c56c7993236c0ebdfe08d110ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b98e8a20e1e3d328265269df6b2927ad.png)
(2)若关于x的不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b80fef6a2dd7e822d83ae45ea79a5357.png)
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06fc1f7733bebb86885b6e6fd0534e1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d8b60555f0d82c386c5b935c23ff952.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12965bbc260bdbb0df0a110e59fb8d78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93bf66ef253242900ca1702121238b14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52dc0bb1b1d25a0e86babc0edc627e44.png)
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解答题-证明题
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【推荐1】对于函数
,若在其定义域内存在实数
,
,使得
成立,称
是“
跃点”函数,并称
是函数
的“
跃点”.
(1)求证:函数
在
上是“1跃点”函数;
(2)若函数
在
上是“1跃点”函数,求实数
的取值范围;
(3)是否同时存在实数
和正整数
使得函数
在
上有2021个“
跃点”?若存在,请求出所有符合条件的
和
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3a51859654d92b5a713bea964091caf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(1)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/053591512cbdc296c8ccd076dd80f7c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e11f4ca0e7ace69f92130d0525bcdb3.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e95b48ab77b279987e3a52e56cab5e3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ab5e0524def52baf53480b8726784ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)是否同时存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb853095f13ee953f77e788f9b75258f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84c6c1e0ea3b81713db2f764eba0e251.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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【推荐2】 设函数
,其中
.
(I)若
是函数
的一条对称轴,求函数周期
;
(II)若函数
在区间
上为增函数,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30aff38b821180c5c321f94dc548e7a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0030fe7eb4f19e2348ab792c9281df19.png)
(I)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84298024ba7686de399a02dc979ee334.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(II)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd301f4c88baf3dbcda01df0e71a7db6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8542e50495795c98f7aa7501fe0690a.png)
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【推荐1】已知函数
,
为常数.
(1)证明:
的图象关于直线
对称.
(2)设
在
上有两个零点
,
.
(ⅰ)求
的取值范围;
(ⅱ)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d572266d7847c48bf451ea5a81a56ec7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec25b105130d71d3d529524671b6218.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6400ec27a77d671d1fcc1d883d525dd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(ⅱ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d036114de7d006d748ca6bb0af07d8e.png)
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【推荐2】已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b5eb70e92964eade3fa79d4f6504891.png)
(1)求函数
的周期和对称轴方程;
(2)若将
的图像上的所有点向右平移
个单位,再把所得图像上所有点的横坐标缩短为原来的
倍(纵坐标不变),得到函数
的图像.若方程
在
上的零点从小到大依次为
,
,
,求
的值;
(3)若方程
在
上的解为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b5eb70e92964eade3fa79d4f6504891.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)若将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49d40807070f239f51276241dbef2f46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1e9fc088559b30adaf3b434c1460446.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef7a6dc30fe8bc0f1cb0642421aea165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf143ca6acd9bafcce6716f4e6f2d9a3.png)
(3)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26e863103315e1808529189383c7770b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71163f419555f2ed76075c8ff659fbfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abc79ae18ef753ee2faf3363efc55c46.png)
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解题方法
【推荐1】已知向量
.
(1)当
时,函数
取得最大值,求
的最小值及此时
的解析式;
(2)现将函数
的图象沿
轴向左平移
个单位,得到函数
的图象.已知
是函数
与
图象上连续相邻的三个交点,若
是锐角三角形,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c921ab3e208d45b41f17ef584751a3b.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70c6cb0cc172657611e286e7fa669584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)现将函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e33b8da413a3b009e3b3a60db3117d25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
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【推荐2】已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/778662c16848db470c6537705b8a839c.png)
若
的最小值为 - 3,求m的值;
当
时,若对任意
都有
恒成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd737219d9b385af861192f4fc18e146.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/778662c16848db470c6537705b8a839c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf6c84731e5e1bd335ecfc2d36c3d81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f53190d6ead827a6338b9de847aeaf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e94f16d5ed858699bfea5039a7bf8ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/239a01bf0f1b5d3926494316d23cf02f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/310e1ebd3ac52132b7e33af907e28624.png)
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