1 . 如果函数
在
处的导数为
,那么
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9434da94e2eb7e3090805b6ed1638c9.png)
A.1 | B.![]() | C.![]() | D.![]() |
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解题方法
2 . 已知函数
.
(1)若
时,求
在
上的最大值和最小值;
(2)若
在
上是减函数,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9404fea0674dedd83a15bbfc7517b645.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cc868a2077000982bd4594d95cfc351.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3af98533fbc91ae52c1eeaf0592a86f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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3 . 已知函数
.
(1)若
,求函数
过点
的切线方程;
(2)证明:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a32e3a1fa4228c15bb163eaf6dfa98d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc30165c18de623d0a3efb961e606d1c.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0976ed8339e2ee25d1aeed44daa637c.png)
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4 . 已知
为自然对数的底数),则a,b,c的大小关系为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75752a24b938876a0eb9523d2729c9ee.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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5 . 某物体的位移
(单位:
)与时间
(单位:
)满足函数关系式
,其中
为常数.若当
时,该物体的瞬时速度为
,则当
时,该物体的瞬时速度为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a454a2c91ace8ef50412a6adf91f8086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/145d1cc09b35092c3f7815f0e409a0cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aeb9a94e392f6759b18abed89aacc5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6196cf17c17eb7b94ef4b963942a0680.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38724fa88a08e6b45a5eb248ca8807b9.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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6 . 已知函数
的导函数为
,并且满足
,则
的值为( )
![](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/31f1069bd96f7e03b4c7da6de305b8e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ad19d1ad05a31122ad5163011c89572.png)
A.![]() | B.3 | C.![]() | D.2 |
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7 . 若曲线
在
处的切线与直线
垂直,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/897c8493f22dd9a52f74433ac4f635ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/367a594caf34ba6686d6540539334a20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
A.3 | B.2 | C.1 | D.0 |
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8 . 已知函数
的图象如图所示,则不等式
的解集为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a07dc1f37fec7a4c98d1eac11cd089a6.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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9 . 现有5种不同的农作物可供下图中的4块地种植,每一块地种一种农作物,且相邻的两块地种的农作物不能相同,若最多使用3种农作物,则不同的种植方法数为_______________ .
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10 . 已知函数
.
(1)若函数
在
处取得极值,对任意的
,不等式
恒成立,求
的取值范围;
(2)若
,讨论方程
根的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7674127664c2b4de3575fe408cd8e9ed.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55aa0a20848c37c1892c567b2315e04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d069aaf35f381e7c69fa78414ff780a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f774138192412cac10b304d4cb666696.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7366e611a86c7b42117661fa361cd76.png)
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