已知函数
,
.
(1)若函数
在点
处切线方程为
,求
,
的值;
(2)当
时,求函数
在
上的最小值;
(3)设
,若对任意
,均存在
,使得
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d827f87e10a7848797480161dcf3cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a1a5f2533b8ea54b7022383f875666.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87aba319e62dd0fe1c2db30759a8ded7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6c1756b564bf1d998d8179637011c88.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bc5e86dbead2bde2fdb2aa0ac6c838f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef7d0bc99c91ce51480ae55134d23db6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a49684ba67f71171321586f1a77ad4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c325eb8d56efe097f20d20c9489a5df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
更新时间:2017-10-07 20:58:14
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解答题-证明题
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适中
(0.65)
名校
解题方法
【推荐1】已知函数
为
的导函数.
(1)若函数
在
处的切线的斜率为2,求
的值;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd89215e2ca32227c59c8abc434b3cb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9d093ec9de55c59fcfc9a585eb8fe12.png)
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【推荐2】若抛物线y=x2与直线2x-y+m=0相切,求切点P的坐标和m的值.
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【推荐1】已知函数
.
(1)求
在
处的切线方程;
(2)当
时,
,
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35117625456b6b99441d0591678ca163.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb788ae88e457017bb81120b6a2e5ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7152aea5d046953a8c931571be7c529.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e41cb6a17af8cf2a2ed28db80770dcd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bee3060ba953107cdf320310f05286a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9faeed172ec5b88966b0d1c52748d41.png)
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【推荐2】已知函数
(
,
为正实数).
(Ⅰ)若
,求曲线
在点
处的切线方程;
(Ⅱ)求函数
的单调区间;
(Ⅲ)若函数
的最小值为
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abd31bc2634fd56977189bada42338c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bec9ff3d82ba1c5f4bf4d217371ddee8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(Ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bea9227dd0104da58e0c40952cc87ed.png)
(Ⅱ)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(Ⅲ)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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【推荐1】已知函数
.
(1)讨论函数
的单调性;
(2)设
,当
时,
,实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c89e647d3fb01eaa1ba32a9c622b895e.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65f1bcf110c36fea39bd22e435e8c6a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6315712bee0070b6ec91ca75d731245e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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【推荐2】已知函数
,
.
(1)讨论
的单调性;
(2)若
,函数
,且对任意
,
恒成立,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f6e204c47a4b3a0c7a40083287bacbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52002ccee39a52435c2f8eee174f7b8d.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83e44b6e0717e3053b17612786b38c48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cc2395f479a7f620dc7a8168f87adef.png)
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【推荐1】已知函数.
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
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(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/676e83dbf0d9e8d81aec3b6880cb9cf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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【推荐2】已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62a6db1248f74ba913acba9b13dd545f.png)
(1)讨论函数
的单调性;
(2)若函数
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,记
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的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62a6db1248f74ba913acba9b13dd545f.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若函数
![](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/0cfa6926b7df5872e57773db15cbd5d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bae872425bced4ed31898663f2feddf9.png)
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