题目
题型:不详难度:来源:
(Ⅰ)函数g(x)=3x-2
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113645-34971.png)
(Ⅱ)函数h(x)=
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113645-14810.png)
G(x)<-2,求实数a的取值范围.
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113645-72222.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113645-96762.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113645-72222.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113645-68697.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113646-39737.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113646-64862.png)
解析
(2)先求出G(x)的表示式,然后本题可转化为以任意x∈(0,1), G(x)max<-2,然后求G(x)的最大值即可.
(Ⅰ)函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113646-80907.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113646-76636.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113646-74950.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113647-23446.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113647-68380.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113647-25393.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113647-95134.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113645-72222.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113647-13039.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113648-23712.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113645-72222.png)
∴函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113645-72222.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113645-96762.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113645-72222.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113645-68697.png)
(Ⅱ)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113648-23559.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113648-30206.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113647-25393.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113648-41509.png)
①当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113648-82654.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113648-19046.png)
②当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113649-45331.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113647-25393.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113649-85521.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113649-69167.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113649-80354.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113647-25393.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113650-99239.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113650-60968.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113650-22059.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113650-52050.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113650-20124.png)
若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113650-69873.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113651-77021.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113651-24934.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113651-42095.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113651-73784.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113652-83632.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113652-71833.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113647-25393.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113650-99239.png)
若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113652-38647.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113652-64540.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113652-48470.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113652-13598.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113653-77986.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113653-16850.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113653-28991.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113653-73121.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113653-19890.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113651-73784.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113654-42703.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113652-71833.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113653-28991.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113654-86680.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113646-39737.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113646-64862.png)
核心考点
试题【已知函数f (x)=lnx.(Ⅰ)函数g(x)=3x-2,若函数F(x)=f(x)+g(x),求函数F(x)的单调区间;(Ⅱ)函数h(x)=,函数G(x)=h(】;主要考察你对函数的单调性与导数等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113635-13949.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113635-84080.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113635-78297.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113627-12804.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113628-82849.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113628-63403.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113628-25456.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113628-63403.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113628-49826.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113629-31596.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113612-82837.png)
(1)试讨论
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113612-19022.png)
(2)如果当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113612-72983.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113613-52988.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113613-77524.png)
(3)记函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113613-89913.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113613-76404.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113614-18663.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113613-77524.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113602-40474.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113602-68641.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113602-84616.png)
(1) 求函数的解析式; (2) 若在区间
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113603-56289.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113603-20402.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113554-32485.png)
(1)若a=3,b=-2,求f(x)在[
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113555-86044.png)
(2)若b=2,f(x)存在单调递减区间,求a的范围.
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