题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050342-99155.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050343-36344.png)
(Ⅰ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050343-99756.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050343-96809.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050343-65015.png)
(Ⅱ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050343-69373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050344-49192.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050344-78964.png)
解析
试题分析:(I)求出导数即切线斜率,代入点斜式;(II)列表,依据参数分情况讨论,求最值.
试题解析:(Ⅰ)解:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050343-69373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050344-53265.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050344-67330.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050343-99756.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050345-44259.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050345-90171.png)
所以曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050343-96809.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050343-65015.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050345-40945.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050344-78964.png)
(Ⅱ)解:方程
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050345-71728.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050346-46206.png)
(ⅰ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050346-80893.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050346-28754.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050343-69373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050346-61358.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050343-69373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050344-49192.png)
上的最小值是
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050346-23699.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050347-61245.png)
(ⅱ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050347-40895.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050345-71728.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050347-65902.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050347-67882.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050343-69373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050348-71357.png)
![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
![]() | ↗ | | ↘ | | ↗ |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050343-69373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050350-45427.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050351-91042.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050351-76960.png)
8分
① 当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050351-24392.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050351-44307.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050343-69373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050346-61358.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050343-69373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050344-49192.png)
上的最小值是
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050346-23699.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050347-61245.png)
② 当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050351-44290.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050352-58651.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050343-69373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050352-34478.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050352-75236.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050343-69373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050344-49192.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050352-30380.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050352-70685.png)
所以 当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050353-56130.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050343-69373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050344-49192.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050347-61245.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050353-49134.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050343-69373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050344-49192.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050346-23699.png)
③ 当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050353-32043.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050353-69829.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050343-69373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050346-61358.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050343-69373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050344-49192.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050347-61245.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050346-23699.png)
综上,
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050354-10380.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050343-69373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050344-49192.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050354-62939.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050354-35732.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050353-56130.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050343-69373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050344-49192.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050354-68262.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050354-35732.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050353-49134.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050343-69373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050344-49192.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050354-68262.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050354-62939.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050353-32043.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050343-69373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050344-49192.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050354-35732.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050354-62939.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050332-92963.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050332-30819.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050333-46419.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050333-59913.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050332-30819.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050333-36020.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050333-32719.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050333-63942.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050333-36482.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050334-31455.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050334-29064.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050334-24433.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050318-83130.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050318-95486.png)
(Ⅰ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050318-38733.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050318-11283.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050319-24536.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050318-38733.png)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050319-54617.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050319-64635.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050319-81409.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050306-65924.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050306-41437.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050306-16248.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050306-88968.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050306-25857.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050306-16617.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050306-61672.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050307-67983.png)
(Ⅰ)求实数a,b的值;
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050307-93613.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050307-10559.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050307-28527.png)
(Ⅲ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050307-35095.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050307-30815.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050307-12773.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050246-92373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050246-48449.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050246-83214.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050247-50853.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050247-86165.png)
(Ⅱ)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050247-13334.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050247-16531.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050248-58729.png)
(Ⅲ)若方程
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050248-54548.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050247-86165.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050223-55078.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050224-53856.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050224-38178.png)
(Ⅰ)讨论
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050224-10967.png)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050224-26553.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050224-78476.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018050225-70284.png)
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