已知函数
.
(Ⅰ)证明曲线
上任意一点处的切线斜率不小于2;
(Ⅱ)设
,若
有两个极值点
,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd53503ff8f6f46508aac59355c92107.png)
(Ⅰ)证明曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(Ⅱ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37b97b295f88972ba1c7e3cefda0885d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba45c507dddd97db9d28eb1633684b16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a02f11d0809b1affec0be90d1bae04b.png)
更新时间:2017-04-20 21:47:02
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相似题推荐
解答题-问答题
|
困难
(0.15)
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解题方法
【推荐1】已知函数
的图象在
处的切线方程为
.
(1)求
,
的值;
(2)若关于
的不等式
对于任意
恒成立,求整数
的最大值.(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1ce4e3971706507d53a3c3cfeb4e956.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8487d2ea7cda0b701db8230d65b4b901.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdf7a0098d4ea8a0ad76dab74698fcb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b8c164755dc2d7cff80fb4c9cffc9be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5369b9dcd2e1126bed3e0b77fa2b709.png)
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【推荐2】如果有且仅有两条不同的直线与函数
的图象均相切,那么称这两个函数
为“
函数组”.
(1)判断函数
与
是否为“
函数组”,其中
为自然对数的底数,并说明理由;
(2)已知函数
与
为“
函数组”,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8fd1e808e015f4cb43d2e3a0529ac6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8fd1e808e015f4cb43d2e3a0529ac6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bea75e6fa8f587c7afff0ffb563b921.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5db192285632d1991b4ee7a003a52205.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a3eda8f315eb3b1e949c7a0989b9bd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30612ee82e71ff4c6f831f1b43c25bf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解答题-问答题
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名校
解题方法
【推荐1】已知函数
,
,其中
,
是
的一个极值点,且
.
(1)讨论函数
的单调性;
(2)求实数
和a的值;
(3)证明
(
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7374847b988fe9d400614d62c191f99a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4483b5a70cf1a8f3410a637f7417a6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee472f4c364364dca231156703ab291.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(3)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b02102099e1d5634ad44717ec6a89576.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
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【推荐2】已知函数
.
(1)若
,讨论
的单调性.
(2)若
有三个极值点
,
,
.
①求
的取值范围;
②求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85aae4eb1df94b4a4ca49560fe6a8c72.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
②求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9b0c4ce20f493a7edf5ca34c571560b.png)
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【推荐3】已知函数
.
(1)当
时,求
的单调区间;
(2)若
有且仅有一个零点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f512ca9ea3d0ca120fda0e1de321c9e.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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