名校
1 . 根据多元微分求条件极值理论,要求二元函数
在约束条件
的可能极值点,首先构造出一个拉格朗日辅助函数
,其中
为拉格朗日系数.分别对
中的
部分求导,并使之为0,得到三个方程组,如下:
,解此方程组,得出解
,就是二元函数
在约束条件
的可能极值点.
的值代入到
中即为极值.
补充说明:【例】求函数
关于变量
的导数.即:将变量
当做常数,即:
,下标加上
,代表对自变量x进行求导.即拉格朗日乘数法方程组之中的
表示分别对
进行求导.
(1)求函数
关于变量
的导数并求当
处的导数值.
(2)利用拉格朗日乘数法求:设实数
满足
,求
的最大值.
(3)①若
为实数,且
,证明:
.
②设
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4a1d0dba29a77dd111efcde543d6c1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc4c14935585e8fa61d032730867d771.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67b6f154c6b2de5695eb1807b98c2c63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/809615d1f91508e2c6c0cda7e592c479.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/244021f826099b18e31af1143597bba2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb5be11a5e6aaf00b2833930b198b4cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0203b006524305c3d8ee0b6c34cd872b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4a1d0dba29a77dd111efcde543d6c1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc4c14935585e8fa61d032730867d771.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1c3c1ed4fb65ab9505ad8078d8d0fb5.png)
补充说明:【例】求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d7ca0caa9933b7afd4bed2683140a07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aebdee8d81b048b5aa520f7e8ba56ff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1e15a54c6122c695239107dd0901bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/244021f826099b18e31af1143597bba2.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b3d9ab2fcf15b94f33cb64f84ed906c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(2)利用拉格朗日乘数法求:设实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c45d8122b61de13875003d00c002c5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de725a9fc66f67abbe0015131846a648.png)
(3)①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a14c388e1e2e5a2ff1ccf6caffbee0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd24c686fbaaa68705d654b880481ffe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e778f95c72fec00bfbbc63e6dfd0c460.png)
②设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/497d269c30eec393e3f0e877ddbe2983.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ade042c085bbad8aeaf111b9f4c33408.png)
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2 . 对于三次函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19951f3364fb04433feed743bc37975d.png)
,给出定义:设
是函数
的导数,
是
的导数,若方程
有实数解
,则称点
为函数
的“拐点”,同学经过探究发现:任何一个三次函数都有“拐点”;任何一个三次函数都有对称中心,且拐点就是对称中心,若
,请你根据这一发现,求:(1)函数
的对称中心为___________ ;(2)计算![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cb8378ae701d9f5a5d66da3cf62c65d.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19951f3364fb04433feed743bc37975d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f5bb89c3ad435f1ef59307b174105ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10acd6d864583617dd3e71240bf0c857.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df1fa6ca9eb7cea9131dad36db6a0ac6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43db00e106c7d08a76a7ba71ca5e63d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7ed163db8f836e5399406e6d8a7fbd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cb8378ae701d9f5a5d66da3cf62c65d.png)
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2021-10-23更新
|
658次组卷
|
10卷引用:北京市第一六一中学2022届高三10月月考数学试题
北京市第一六一中学2022届高三10月月考数学试题江苏省淮安市高中校协作体2021-2022学年高三上学期期中联考数学试题(已下线)第1讲 函数的图象与性质(练 )-2022年高考数学二轮复习讲练测(新教材·新高考地区专用)(已下线)考向08 函数的奇偶性、周期性与对称性(重点)(已下线)第24讲 章末检测四-备战2023年高考数学一轮复习考点帮(新高考专用)江苏省徐州市第七中学2022-2023学年高三上学期12月学情检测数学试题江苏省盐城市大丰区新丰中学2022-2023学年高二上学期期末数学试题(已下线)宁夏石嘴山市第三中学2023-2024学年高二上学期期末数学试题(已下线)期末考试押题卷一(考试范围:苏教版2019选择性必修第一册)-【帮课堂】2023-2024学年高二数学同步学与练(苏教版2019选择性必修第一册)江苏省南菁高级中学2023-2024学年高二下学期5月月考数学试题
3 . 对于三次函数
,定义:设
是函数
的导数
的导数,若方程
有实数解
,则称点
为函数
的“拐点”,有同学发现“任何一个三次函数都有‘拐点’;任何一个三次函数都有对称中心;且‘拐点’就是对称中心.”根据此发现,若函数
,计算![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7c49c695bacd61623b2345f40b7694a.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75044e0301ef9def5c1a1c8e6f2cba77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02639813b0ea2d5b097bf496bed88af0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a673c4b255a76a31893c53b4e8c3420b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/941e6b1b32d3f7fc5586252d838c9924.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0573a6bcc480a91a43126d01bc19eeae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f40d352eec1bf856772b11c469ccfa9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7c49c695bacd61623b2345f40b7694a.png)
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解题方法
4 . 对于三次函数
,给出定义:设
是函数
的导数,
是
的导数,若方程厂
有实数解
,则称点
为函数
的“拐点”.某同学经过探究发现:任何一个三次函数都有“拐点”;任何一个三次函数都有对称中心,且拐点就是对称中心,若
,则该函数的对称中心为__________ ,计算![](https://staticzujuan.xkw.com/quesimg/Upload/formula/548eb858131e44c6d2a1adf359b3d38c.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/012429b7101ba0f84e7b45598ed12db9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10acd6d864583617dd3e71240bf0c857.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df1fa6ca9eb7cea9131dad36db6a0ac6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43db00e106c7d08a76a7ba71ca5e63d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/155d61774bc044c666368e15c0e83390.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/548eb858131e44c6d2a1adf359b3d38c.png)
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5 . 对于三次函数
,定义:设
是函数
的导数
的导数,若方程
有实数解
,则称点
为函数
的“拐点”,有同学发现“任何一个三次函数都有‘拐点’;任何一个三次函数都有对称中心;且‘拐点’就是对称中心.”根据此发现,若函数
,计算![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21adb23350026638d3094245b093acef.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75044e0301ef9def5c1a1c8e6f2cba77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02639813b0ea2d5b097bf496bed88af0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a673c4b255a76a31893c53b4e8c3420b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/941e6b1b32d3f7fc5586252d838c9924.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0573a6bcc480a91a43126d01bc19eeae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f40d352eec1bf856772b11c469ccfa9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21adb23350026638d3094245b093acef.png)
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2018-07-17更新
|
673次组卷
|
2卷引用:【全国市级联考】山东省德州市2017-2018学年高二下学期期末考试数学(理)试题
6 . 对于三次函数
.定义:①
的导数为
,
的导数为
,若方程
有实数解
,则称点
为函数
的“拐点”;②设
为常数,若定义在
上的函数
对于定义域内的一切实数
,都有
恒成立,则函数
的图象关于点
对称.
(1)已知
,求函数
的“拐点”
的坐标;
(2)检验(1)中的函数
的图象是否关于“拐点”
对称.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/012429b7101ba0f84e7b45598ed12db9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10acd6d864583617dd3e71240bf0c857.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df1fa6ca9eb7cea9131dad36db6a0ac6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43db00e106c7d08a76a7ba71ca5e63d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abde3621d19a60d8b0cad42c06d8891.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43db00e106c7d08a76a7ba71ca5e63d1.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03d5f97843013ef486e10f66543562a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)检验(1)中的函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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名校
7 . 对于三次函数
.定义:①
的导数为
,
的导数为
,若方程
有实数解
,则称点
为函数
的“拐点”;②设
为常数,若定义在
上的函数
对于定义域内的一切实数
,都有
恒成立,则函数
的图象关于点
对称.
(1)已知
,求函数
的“拐点”
的坐标;
(2)检验(1)中的函数
的图象是否关于“拐点”
对称;
(3)对于任意的三次函数
写出一个有关“拐点”的结论(不必证明).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/012429b7101ba0f84e7b45598ed12db9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10acd6d864583617dd3e71240bf0c857.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df1fa6ca9eb7cea9131dad36db6a0ac6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43db00e106c7d08a76a7ba71ca5e63d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abde3621d19a60d8b0cad42c06d8891.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43db00e106c7d08a76a7ba71ca5e63d1.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03d5f97843013ef486e10f66543562a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)检验(1)中的函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(3)对于任意的三次函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/012429b7101ba0f84e7b45598ed12db9.png)
您最近一年使用:0次
8 . 已知函数
.
(1)求函数
在
处的切线方程;
(2)若
是
的极值点,且方程
有3个不同的实数解,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66aa600e8ebc54042affceac4efeaeb7.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e31bc0c34811edba74dae3fcaed8f577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2023-07-08更新
|
604次组卷
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3卷引用:广东省东莞市2022-2023学年高二下学期期末数学试题
9 . 对于三次函数
,定义:设
是函数
的导函数
的导数,若
有实数解
,则称点
为函数
的“拐点”.现已知
.请解答下列问题:
(1)求函数
的“拐点”A的坐标;
(2)求证:
的图像关于“拐点”A对称,并求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75044e0301ef9def5c1a1c8e6f2cba77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47db775f5675cd10012f964a336832f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4a5292f6af433342a866336d05fe5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de68bc1a57041a038aea6711c8848999.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43db00e106c7d08a76a7ba71ca5e63d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa4724249ffd113d05e9a1806c90647e.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44497598c08c9e219a7737af9faa1d87.png)
您最近一年使用:0次
2022-09-30更新
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520次组卷
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6卷引用:河南省南阳市第一中学校2022-2023学年高三上学期第二次阶段考试文科数学试题
河南省南阳市第一中学校2022-2023学年高三上学期第二次阶段考试文科数学试题山西省晋中市平遥县第二中学校2023届高三上学期10月月考数学试题(已下线)1.2.2 函数的和差积商求导法则(同步练习)2022-2023学年高二选择性必修第二册素养提升检测(提高篇)(已下线)5.2 导数的运算(2)(已下线)第01讲 导数的概念与运算-【寒假预科讲义】2024年高二数学寒假精品课(人教A版2019)(已下线)2023-2024学年高二下学期第一次月考解答题压轴题十六大题型专练(1)
12-13高三上·江苏扬州·阶段练习
解题方法
10 . 对于三次函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cbb68078590e8785def6cb1d7e0126a.png)
.
定义:①设
是函数
的导数
的导数,若方程
有实数解
,则称点
为函数
的“拐点”;
定义:②设
为常数,若定义在
上的函数
对于定义域内的一切实数
,都有
成立,则函数
的图象关于点
对称.
已知
,请回答下列问题:
(1)求函数
的“拐点”
的坐标
(2)检验函数
的图象是否关于“拐点”
对称,对于任意的三次函数写出一个有关“拐点”的结论(不必证明)
(3)写出一个三次函数
,使得它的“拐点”是
(不要过程)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cbb68078590e8785def6cb1d7e0126a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f2b5ee1eabb64358a3d9db2349b6fce.png)
定义:①设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aac282e92da3691942a6ba8511de2303.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d31f9ce464f2ce3b24833b70595941c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc581690f1d82133bb5fed3d7f365f2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/641790f25de4850d4dde3e370db820c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
定义:②设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/905b9677c88be032f6f283ea9194f2b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/641790f25de4850d4dde3e370db820c6.png)
已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec5a67c1baa2a00e8edf1cda8c932203.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)检验函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(3)写出一个三次函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92860378096f519a8fb276d07dbfabce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a7e88b74f492f89e21e4cf65353bdb6.png)
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