jin_zhang813
幼苗
共回答了16个问题采纳率:93.8% 举报
(1)
![](https://img.yulucn.com/upload/c/47/c475a3674a209159b52c2aef8684bc8a_thumb.jpg)
. (2)
![](https://img.yulucn.com/upload/a/0f/a0fd6dcd778231f45d3f20a6d5ab35e2_thumb.jpg)
. (3)
![](https://img.yulucn.com/upload/d/e2/de2bd69e5e22ea3551b90b58adb135a4_thumb.jpg)
.
解决不等式恒成立问题,常用的方法是分离出参数,构造新函数,求出新函数的最值,得到参数的范围.
(I)求出g(x)的导函数,令导函数小于0得到不等式的解集,得到相应方程的两个根,将根代入,求出a的值.
(II)求出g(x)的导数在x=-1的值即曲线的切线斜率,利用点斜式求出切线的方程
(III)求出不等式,分离出参数A,构造函数h(x),利用导数求出h(x)的最大值,令a大于等于最大值,求出a的范围.
解:(1)
![](https://img.yulucn.com/upload/3/51/3511360d3b72869bdd23885bc3c5dec9_thumb.jpg)
………………………1分
由题意
![](https://img.yulucn.com/upload/6/e7/6e79816a62b31095fa78def3bffd38c9_thumb.jpg)
的解集是
![](https://img.yulucn.com/upload/7/a3/7a3b5fa5e8978cbf1ffaed8af143c281_thumb.jpg)
即
![](https://img.yulucn.com/upload/7/08/708f9592040f2372a4d5d7f2b65f4104_thumb.jpg)
的两根分别是
![](https://img.yulucn.com/upload/7/b2/7b22cd001cb396ebe2399e40d01547c6_thumb.jpg)
.
将
![](https://img.yulucn.com/upload/c/de/cdeb2af38de160ca19cabe07e38d7964_thumb.jpg)
或
![](https://img.yulucn.com/upload/0/cb/0cbc356fef4fb36cb94c14a1723e78f8_thumb.jpg)
代入方程
![](https://img.yulucn.com/upload/7/08/708f9592040f2372a4d5d7f2b65f4104_thumb.jpg)
得
![](https://img.yulucn.com/upload/6/6b/66b6f2cf6bd9c788ea98fee3fab8e032_thumb.jpg)
.
![](https://img.yulucn.com/upload/c/47/c475a3674a209159b52c2aef8684bc8a_thumb.jpg)
. …………4分
(2)由(Ⅰ)知:
![](https://img.yulucn.com/upload/4/58/4588b061fb53ad81902fcac8e55a5d7a_thumb.jpg)
,
![](https://img.yulucn.com/upload/f/a3/fa3e782701504c8d59f4c93b5975a8c0_thumb.jpg)
,
![](https://img.yulucn.com/upload/c/39/c39d99ef745dee9d4f5af9f686e39b51_thumb.jpg)
点
![](https://img.yulucn.com/upload/7/e6/7e6a42e91653a687f327b652e895fa84_thumb.jpg)
处的切线斜率
![](https://img.yulucn.com/upload/4/0f/40fb46dfa503f793e82a0e967c4580f8_thumb.jpg)
,
![](https://img.yulucn.com/upload/c/39/c39d99ef745dee9d4f5af9f686e39b51_thumb.jpg)
函数y=
![](https://img.yulucn.com/upload/5/ed/5ed8f4d06a5e31be5877fc38da802af5_thumb.jpg)
的图像在点
![](https://img.yulucn.com/upload/7/e6/7e6a42e91653a687f327b652e895fa84_thumb.jpg)
处的切线方程为:
![](https://img.yulucn.com/upload/5/c6/5c6e8cf16d1383aaec7fb6e2e0783d97_thumb.jpg)
,即
![](https://img.yulucn.com/upload/a/0f/a0fd6dcd778231f45d3f20a6d5ab35e2_thumb.jpg)
. …………7分
(3)
![](https://img.yulucn.com/upload/0/b7/0b7a1a4ad6cdd62289f40658ca456329_thumb.jpg)
,
![](https://img.yulucn.com/upload/2/1e/21e8c01ec2deeb0bd58747d9d9c72d3f_thumb.jpg)
即:
![](https://img.yulucn.com/upload/d/ec/dec0c8fc3215db7e8dd4d4b899e4eb81_thumb.jpg)
对
![](https://img.yulucn.com/upload/c/c4/cc46f5fd0ba18447a315a054f0619833_thumb.jpg)
上恒成立
可得
![](https://img.yulucn.com/upload/b/0f/b0f733a81a5f0997302b2693aaabdbda_thumb.jpg)
对
![](https://img.yulucn.com/upload/c/c4/cc46f5fd0ba18447a315a054f0619833_thumb.jpg)
上恒成立……9分
设
![](https://img.yulucn.com/upload/7/9e/79e0adedd6eb900437b665ed0dc4993e_thumb.jpg)
,则
令
![](https://img.yulucn.com/upload/2/1d/21d442d51d6e638b7ce7d7621dfbf8a0_thumb.jpg)
,得
![](https://img.yulucn.com/upload/1/37/1372933432c051d1e9f28db723f5f168_thumb.jpg)
(舍)
当
![](https://img.yulucn.com/upload/0/88/08861852acc7fdc555158d8192365868_thumb.jpg)
时,
![](https://img.yulucn.com/upload/e/b1/eb1f91a6caf7beac94d5b56cae42a13b_thumb.jpg)
;当
![](https://img.yulucn.com/upload/5/cd/5cded2f77ade0fb8840a07248c3d9af1_thumb.jpg)
时,
![](https://img.yulucn.com/upload/9/25/9253744a30734f793510425fb3e0cbff_thumb.jpg)
………..12
![](https://img.yulucn.com/upload/c/39/c39d99ef745dee9d4f5af9f686e39b51_thumb.jpg)
当
![](https://img.yulucn.com/upload/c/de/cdeb2af38de160ca19cabe07e38d7964_thumb.jpg)
时,
![](https://img.yulucn.com/upload/0/c7/0c7b52a8f0706b0a65b96e0ed304b70c_thumb.jpg)
取得最大值,
1年前
1