题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104902-74313.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104902-25930.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104902-30379.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104902-59242.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104903-65770.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104903-20722.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104903-90217.png)
(3)设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104903-78644.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104903-89670.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104904-58562.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104904-69117.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104904-47924.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104903-90217.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104904-49169.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104905-22399.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104905-91825.png)
解析
试题分析:(1)由题意,
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104905-38962.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104905-76265.png)
∴当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104906-98479.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104906-50346.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104906-69656.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104906-56636.png)
所以,
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104902-59242.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104906-33431.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104907-73197.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104904-49169.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104907-66744.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104907-48196.png)
由于
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104907-34073.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104905-22399.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104908-32738.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104905-22399.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104908-49824.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104905-22399.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104908-39688.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104908-84853.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104905-22399.png)
(3)构造函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104908-85606.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104909-14002.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104909-10783.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104909-15985.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104909-63244.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104910-66554.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104910-26708.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104910-53462.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104910-45198.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104911-16378.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104909-10783.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104911-12024.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104911-14316.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104911-54302.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104905-22399.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104911-51193.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104910-66554.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104912-26715.png)
所以要在
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104910-66554.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104912-46127.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104912-80156.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104912-92981.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104913-44606.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104908-84853.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104905-91825.png)
另法:(Ⅲ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104913-30502.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104913-62637.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104913-91243.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104913-53934.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104914-35834.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104914-57988.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104914-92130.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104914-59908.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104914-80726.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104915-41955.png)
综上,要在
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104910-66554.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104915-89596.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104915-65579.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104915-27561.png)
点评:纵观历年高考试题,利用导数讨论函数单调区间是函数考查的主要形式,是高考热点,是解答题中的必考题目,在复习中必须加强研究,进行专题训练,熟练掌握利用导数判断函数单调区间的方法,总结函数单调性应用的题型、解法,并通过加大训练强度提高解题能力.
核心考点
试题【已知,函数.(1)求的极值;(2)若在上为单调递增函数,求的取值范围;(3)设,若在(是自然对数的底数)上至少存在一个,使得成立,求的取值范围。】;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/20191018/20191018104844-35267.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104844-69367.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104845-12306.png)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104845-96653.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104845-12306.png)
(3)若对任意
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104845-87076.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104845-29050.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104845-47548.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104845-33004.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104812-44425.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104812-70544.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104813-23753.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104813-90960.png)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104813-69556.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104813-83681.png)
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104814-24388.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104814-27076.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104814-92636.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104756-56961.png)
(Ⅰ)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104756-42754.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104756-28484.png)
(Ⅱ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104757-20949.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104756-28484.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104757-91626.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104757-72305.png)
(1)若f(x)在x∈[1,+∞)上是增函数,求实数a的取值范围;
(2)若x=3是f(x)的极值点,求f(x)在x∈[1,a]上的最小值和最大值.
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104730-32509.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104730-54774.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104730-10519.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104731-36664.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104731-63088.png)
(I)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104731-34522.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104731-20615.png)
(II)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104732-14511.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104732-40359.png)
(III)若对任意的
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104732-20543.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104732-40359.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104732-24586.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018104732-30271.png)
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