已知函数
.
(1)若
,讨论
的单调性;
(2)若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d2067b63676e9038862fb9428b32ee3.png)
(i)证明
恰有两个零点;
(ii)设
为
的极值点,
为
的零点且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e322555213e8aea91e1ad92bd1070d8f.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb5f421939ee855f25927e7570d82c71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d2067b63676e9038862fb9428b32ee3.png)
(i)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(ii)设
![](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/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64df36fd0b37b72d36fe21e10f5d67f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2271d27dde0895baf5f1f7872168558.png)
22-23高三上·河北石家庄·阶段练习 查看更多[3]
更新时间:2022-12-06 14:45:38
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解答题-问答题
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(0.4)
名校
【推荐1】已知
.
(1)求函数
的单调区间;
(2)若函数
有两个零点
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/233aa8bb190d5535f84eade0cfbc6b95.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/786999ff39b91fac93044fb70679be5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8112293429caa01e7670ebcaf5bf95de.png)
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【推荐2】已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8041f337c8aeaa30ed3c8a74b690c13a.png)
(1)当
时,求函数
在区间
上最大值和最小值;
(2)令
,当函数
恰有两个极值点时,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8041f337c8aeaa30ed3c8a74b690c13a.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35dc21e08edcf00a7596c2ca9f551339.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d18d399ea2799c8731d62b660d88243.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e03ad0c315806342d6cd732a0b91a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
【推荐1】已知函数
,曲线
在
处的切线方程为
.
(1)求
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(2)求函数
在
上的最大值;
(3)证明:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ea764080dd9860df23c7022ca914ea6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac490af25fb49d4f880bbac29a0ee874.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304226ca50149b49702928e44d565964.png)
(3)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/302b30eb9868d1ed08e5f149f18ede1c.png)
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【推荐2】已知函数
,
为函数
的导函数.
(1)讨论函数
的单调性;
(2)若
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdf00355264b2e08b1cf71b601f4a48c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07a9c6e50346f506758635274684eca5.png)
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【推荐1】已知函数
.
(1)若曲线
在点
处的切线方程为
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(2)若
,证明:
在区间
内有唯一的零点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e30671f198b6db7d59cd6d4cf3443299.png)
(1)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/606e5694c2f33033cced4e29d3152c16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf65191643885842f4cb52d8b28e44fa.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6455e38ff53ede2508e4d9cb23f0b86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e1c9c97de9198d47306216e9961b80.png)
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(0.4)
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【推荐2】已知函数
,其中e为自然对数的底数.
(1)讨论函数
的单调性;
(2)用
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中较大者,记函数
.若函数
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42eab567d3a444bf40a7bc00318a424b.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1bfb9487f824ff9fd2a1a281f8d62f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61887f8af16f813e2ac10868ad88c262.png)
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【推荐3】已知函数
,向量
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(1)求
的极值;
(2)判断
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内的零点个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec7d1d6fb2edf55d797d4baf655efc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ad709331cae1fd5a425cba913277d0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68f7584d516c597c5bda82386ffdd717.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b993479717dfbc389dede000156994e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09fee0e4f79e30bbff8e4be338f6adec.png)
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