题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031400-72996.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031400-78685.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031400-24508.png)
(2)若直线
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031400-86642.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031401-37867.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031401-84021.png)
(3)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031401-59097.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031401-27511.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031402-81155.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031402-19928.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031402-36943.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031402-15538.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031402-17185.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031403-53022.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031403-48634.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031403-42706.png)
解析
试题分析:
(1)利用导数可以求解函数单调性得到极值与最值,但是函数含有参数,故而需要讨论,首先对函数求定义域,求导可以发现导函数的分母恒大于0不影响导函数符号,故考虑分子大于0,小于0的解集,讨论a的范围得到区间
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031403-70610.png)
(2)设出切点坐标,利用切点满足的三个条件(①切点在原函数上,坐标满足原函数方程 ②切点在切线上,坐标满足切线方程 ③原函数在切点处的导数为切线的斜率)建立关于a的方程,解方程求出a的值.
(3)由(2)的结论得到此时直线
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031404-50040.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031404-92610.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031404-16067.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031404-50040.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031403-70610.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031404-30632.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031404-87463.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031405-32326.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031403-48634.png)
试题解析:
(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031405-42900.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031405-61772.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031405-65346.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031406-23118.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031406-94224.png)
(ⅰ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031406-65431.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031406-70325.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031406-33090.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031407-38428.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031407-49011.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031403-70610.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031402-15538.png)
(ⅱ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031407-47599.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031406-70325.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031407-25071.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031407-38428.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031407-49011.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031403-70610.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031407-76878.png)
(ⅲ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031406-94224.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031408-31620.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031408-74169.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031408-94390.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031408-12776.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031409-84098.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031409-31334.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031407-49011.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031403-70610.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031409-18314.png)
(2)设切点为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031409-91283.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031410-74356.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031410-56949.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031410-33990.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031410-44967.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031410-96989.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031411-26600.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031411-51035.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031411-27621.png)
由①、②解得
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031402-17185.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031403-53022.png)
(3)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031402-17185.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031411-14063.png)
由(2)的结论直线
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031404-50040.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031404-92610.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031411-73361.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031409-31334.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031412-60522.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031404-50040.png)
根据图像分析,曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031404-16067.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031404-50040.png)
下面给出证明:当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031406-70325.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031412-65836.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031412-38708.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031412-73640.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031409-31334.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031406-70325.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031413-60061.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031412-65836.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031407-38428.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031413-94140.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031413-43966.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031413-83151.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031409-31334.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031413-32568.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031414-82978.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031408-31620.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031414-30751.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031414-47640.png)
且
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031414-59857.png)
因此,
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031403-48634.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031403-42706.png)
核心考点
举一反三
A.y′=sin(2x+1) |
B.y′=-2xsin(2x+1) |
C.y′=-2sin(2x+1) |
D.y′=2xsin(2x+1) |
A.![]() | B.![]() | C.![]() | D.![]() |
A.f(x)=ex | B.f(x)=x3 |
C.f(x)=lnx | D.f(x)=sinx |
A.2 | B.-![]() | C.4 | D.-![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031337-29055.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031337-43114.jpg)
A.2 | B.-![]() | C.3 | D.-![]() |
最新试题
- 1△ABC 的三个顶点坐标的横坐标乘以-1 ,纵坐标不变,则所得图形与原图的关系是[ ]A.关于x轴对称 B.关于
- 2有人站在高土坡上对着输电线拉尿触电身亡,这说明尿液中一定含有导电的( )A.分子B.原子C.离子D.电子
- 3下列方程中,是二元一次方程的有( )A.6x-2=5z+13+6xB.1x+1y=5C.xy+3x+y=1D.x=2y
- 4下表反映了我国四个省区煤炭、太阳辐射能、天然气、水能四种资源的丰歉程度(★号越多代表资源分布越丰富),据此回答下列各题。
- 5—What a big box! Can I help you?—No, thanks. There’s
- 6能量在食物链的流动过程中被多种生物逐步______,生态系统中的植物必须不断的从外界__________________
- 7如图所示是4×4的正方形网格,△ABC的顶点在正方形网格的顶点上,请在4×4的正方形网格上画出一个三角形和△ABC相似但
- 8宿迁市为了打造“楚风水韵,生态绿都”,让宿迁的湖更清、树更绿,2008年市委、市政府提出了确保到2010年实现全市城市绿
- 9“人的思维的最本质和最切近的基础,正是人所引起的自然界的变化,而不单独是自然界本身。” 这表明A.思维与存在具有同一性,
- 102010年4月20日,由于英国石油公司租用的“深水地平线”钻井平台工人操作不慎,一个海底甲烷气泡由钻杆底部高压处向低压处
热门考点
- 1仔细观察下面两幅图,图中的情景反映了什么的兴旺发达( )A.元杂剧B.宋词C.唐诗D.明清小说
- 2(14)设向量,,若,则
- 3一个角的内部从顶点引出4条射线,则此时构成的角的个数有[ ]A.5个B.6个C.10个D.15个
- 4如果5个数x1,x2,x3,x4,x5的方差为7,那么3x1+2,3x2+2,3x3+2,3x4+2,3x5+2,这5个
- 5(8分)用系统命名法给下列物质命名:(1) CH3CH(C2H5)CH(CH3)2___________________
- 6想象一下五十年后我们的家乡会有什么变化。小题1:There will be ______________________
- 7根据提示完成下面表格。(10分)
- 8不同商品对价格变动的反应程度不同,受价格变动影响较大的有( )①生活用品 ②生产用品 ③生活必需品 ④高档耐用品A.
- 9求z=3x+5y的最大值和最小值,使式中的x、y满足约束条件
- 10下列关于有机化合物的性质说法正确的是A.棉花和蛋白质都是高分子化合物,水解产物相同B.苯和乙烯都能使溴水退色,均与溴水发