题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023138-90151.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023138-23880.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023138-32404.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023139-56217.png)
(2)已知点
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023139-31154.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023139-56217.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023139-70274.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023139-53705.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023140-31508.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023140-38059.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023140-57777.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023140-47769.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023140-43552.png)
解析
试题分析:(1)先求导,再令导数等于0,解导数大于0得函数的增区间,解导数小于0得函数的减区间。(2)可将问题转化为在
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023141-51637.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023141-99595.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023141-51637.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023141-11647.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023141-52037.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023142-80772.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023142-98399.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023142-36768.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023141-51637.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023142-68932.png)
解:⑴ 当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023138-32404.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023142-35525.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023143-91985.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023143-39752.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023143-13855.png)
所以当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023138-32404.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023143-55404.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023143-67085.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023144-13871.png)
⑵ 因为对任意
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023144-60322.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023140-31508.png)
所以对任意
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023144-60322.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023140-31508.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023144-96154.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023144-74437.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023143-55404.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023145-81172.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023145-86305.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023145-88317.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023145-13576.png)
①当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023146-42522.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023146-19472.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023146-73851.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023146-86228.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023146-42522.png)
②当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023146-40980.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023147-11911.png)
且
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023147-44006.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023147-78750.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023147-45464.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023148-85643.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023148-78346.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023143-55404.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023143-91985.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023143-55404.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023146-73851.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023148-47111.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023146-40980.png)
⑶ 当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023148-37680.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023148-59118.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023149-45511.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023149-64448.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023149-28050.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023149-71036.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023149-56433.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023150-57803.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023150-74892.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023150-11838.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023150-24889.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023150-11838.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023151-78763.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023151-62160.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023151-21043.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023151-53200.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023152-43333.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023152-97349.png)
综上
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023152-41518.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023127-90039.png)
(1)若保持其缺口宽度不变,求裁剪后梯形缺口面积的最小值;
(2)若保持其缺口深度不变,求裁剪后梯形缺口面积的最小值.
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023127-21880.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023119-49360.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023119-77333.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023119-11430.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023102-56829.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023102-97651.png)
(1)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023102-89863.png)
(2)函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023102-68363.png)
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023102-93833.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023103-19329.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023103-65295.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023044-14664.png)
(1)设函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023044-62778.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023045-41899.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023045-33433.png)
(2)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023045-59017.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023045-92826.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023046-35306.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023032-99742.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023032-60395.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023032-50225.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023033-82569.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018023033-59614.png)
A.![]() | B.![]() | C.![]() | D.不确定 |
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