解题方法
1 . 如图,在平面直角坐标系
中,角
的始边为
轴的非负半轴,终边与单位圆
交于点
,过点
作
轴的垂线,垂足为
.若记点
到直线
的距离为
,则
的极大值点为___ ,最大值为___ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a998a7d4d980e848ee050b706480ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c1ba6b6ee00c4b2763cb3fa59caa69f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c1ba6b6ee00c4b2763cb3fa59caa69f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/9/51345267-addf-40fa-b2c9-9b2fd7dca4d9.png?resizew=165)
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2 . 已知函数
,其中
.
(1)当
时,求曲线
在点
处的切线方程;
(2)若
在
上存在极值,求实数
的取值范围:
(3)写出
的零点个数.(直接写出结论即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f6fd0297d13ef19b5203a5ce1fb698a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40e72f6b2ef3329828cb8fc873eeba7c.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/150e8e4ca6aa729a72a6a17c36b8ebfe.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/879234adbae93aa72b7e101b3738d4e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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3 . 设
,
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8765fd52679051a64500908df4286271.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b6c2bbedfb844b5ac6f0d0058919d45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04a81496ff746bf33de95ee6f20cf154.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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4 . 已知复数
满足
,则复数
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc5719b7583889fddc63cb833ccb08b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7e0aeeb125cfb42e33094594d4381f5.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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5 . 已知函数
.
(1)求曲线
在点
处的切线方程;
(2)设函数
.
①若
在
处取得极大值,求
的单调区间;
②若
恰有三个零点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5bb46545c1d19d4e7a7a250a80f3feb.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9f8845aa2b51c460f2d798c9f62fa3.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89522349eef58c2b645bdc7e0e410749.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
6 . 已知函数
.
(1)若
,求曲线
在
处的切线方程;
(2)若
,求证:函数
在
上有极大值
,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a911465a3dfab7c86341dbe498f92ab8.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5095a28bb1b91bf6bed9e2cfbd76bb18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9f8845aa2b51c460f2d798c9f62fa3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/162a61c6f527d763ed9b5a1f53dc990e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38981c93569ffee5b70f6371de6a88b7.png)
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7 . 若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be5cf942aefbfa7cdc86751b8c45c3ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/882bff376e1d71865bd23b747ef78a66.png)
A.![]() | B.1 |
C.![]() | D.2 |
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8 . 已知函数
.
(1)若曲线
在点
处的切线平行于
轴,求实数
的值;
(2)求函数
的单调区间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eb93a0a7f5e9ffb7dda01d9b9add05c.png)
(1)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bea9227dd0104da58e0c40952cc87ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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名校
9 . 已知函数
.
(1)求曲线
在点
处的切线方程;
(2)求证:当
时,
;
(3)设实数
使得
对
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e5b49c94242af1eccf6990961a9292a.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/691696e19e95dad2695ed99682bcb48e.png)
(2)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f47d8074365c6e643aa10d23f7e7853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/538fa4eef13f50a43a25333ae2b087ad.png)
(3)设实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e779ed8ae49055d4f2e373962ce1cab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f47d8074365c6e643aa10d23f7e7853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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10 . 已知复数
,
在复平面内的对应点关于虚轴对称,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a9a1083238c4121ce5bdf885fb62003.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de3df224d6d20a6fadeded0e810c02b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10a7a554c7e1a2ea005c5a093f6f4666.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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