函数导数三角函数

函数导数三角函数

函数、导数、三角函数回归基础与基本题型复习一、基础知识与基本方法

函数部分 221、二次函数?三种形式:一般式f(x)=ax+bx+c;顶点式f(x)=a(x-

h)+k;零点式f(x)=a(x-x)(x-x);b=0偶函数;?区间最值:配方后一看开口方向,二讨论对称12

轴与区间的相对位置关系;?实根分布:先画图再研究?>0、轴与区间关系、区间

端点函数值符号;

2、值域(范围)常用分子常数法;分离;，分母整体换元;导数

3、周期:进退几

个单位，列举;画图;用周期定义逐个检验; 4、求定义域:使函数解析式有意义(如:分母?;偶次根式被开方数?;对数真数?，底数?;零指数幂的底数?);实际问题有意义; (定义域优先意识) 5、单调性:?定义法;?导数法?图像;奇偶性:?定义法?图像。函

数

2yxx,,，log(2)的单调递增区间是.(答:) (1,2)12

注意:(1)函数单调性与奇偶性的逆用(?比较大小;?解不等式;?求参数范围(注

意等号)); 依据单调性，利用一次函数在区间上的保号性可解决求一类参数的范围问题:(或fugxuhx()()()0,，,

fa()0,,fa()0,,(或); ,,,,0)()aub,,fb()0,fb()0,,,2若存在?[1，3]，使得

不等式，(-2)-2>0成立，则实数取值aaxaxx范围是 (

22解:不等式即，设.研究“任意a?()220xxax，,,,faxxax()()22,，,,

f(1)0,,2，，[1，3]，恒有”.则，解得。则实数x的取值范围是

fa()0,x,,1,,,,f(3)0,3，，,

2,, ,,,,，,,1,，，,,3,,

(2)复合函数由单调性判定:同增异减。

6(常见的图象变换——平移、伸缩、对称 (类比三角函数);掌握函数axbbaca，,yabacyxa,,，,,,，,(0);(0)的图象和性质; xcxcx，，

7、恒成立问题:分离参数法;最值法;化为一次或二次方程根的分布问题.a?f(x)

,,恒成立a?[f(x)];a?f(x)恒成立a?[f(x)];;区分有解与空集;方程max,min k=f(x)有解k?D(D为f(x)的值域); ,

8、奇偶性:若f(x)是偶函数，那么f(x)=f(,x)=;若f(x)是奇函数，0在其定

f(x)

义域内，则(可用于求参数);奇函数在对称的单调区间内有相同的单f(0)0,

调性;偶函数在对称的单调区间内有相反的单调性;若所给函数的解析式较为复杂，应先化简，再判断其奇偶性;判断函数奇偶性可用定义的等价形式:f(x)?

f(,x),,1f(-x)=0或(f(x)?0); f(x)

9、对于以下类型的问题需要注意:

y,a2222可分别通过构造距离(4)F(cos,,sin,);(5)a,ab，b;(1)(x,a)，

(y,b);(2);(3)Ax，By;x,b

22函数、斜率函数、截距函数、单位圆x+y=1上的点及余弦定理进行

(cos,,sin,)village temples Central Office every day, carry out their duties. Correspondence relating to education by the Chief of the first section marked my draft statement. Worked after a few months, I've been buried in the official program, very rigid monotony of clerical career, flavourless. 1939 of 7 August between, County, and Secretary to I with

to Office meeting, for Government established one years to work reported, for time rush, prior not for full prepared, had to in way by rank Ann Mr described one years to about people, and fiscal, and built, and taught, and insurance five aspects important matters, I accordingly detailed

narrative finishing written, completed Wujiang Government established one years to of work report. Turn back and forth month Shan Road, apart from the Secretary, Mr rank foot disease immobility, bamboo car instead of walking outside, square foot (except for myself and 4 guards), the wuxing, peace, SI an, Guangde, doorway swing, Zhang Zhu to the destination--wearing Bu. At diwei to the important towns of troops is difficult to access, we have to change angles, Shan rugged trails, Sun and rain on the way, hardship exceptions, if the patriotic and passions of the war, than the successful completion of tasks. An old frail, rank, long-distance Lawton regrets, admirable! In November 1939, I was admitted to the Faculty of law, College of law and politics in Shanghai, but resigned from the post office, bid farewell to this short and memorable life. (J) the siazhen boat buried Japanese morning of October 18, 1937, siazhen sick to shun Tang Qiao-cutters, 1 from Nanxun town jiaxing to Japanese boats, caught dragging behind 3 small boats, loaded with military goods. Siazhen too late to escape, jumped ashore Japan catch up with the boat, forcing him to row a boat. Meanwhile caught the migrants village Zhang Shun. Siazhen was sick for a long time, 转化达到解题目的。

导数部分 /1、导数几何物理意义:k=f(x)表示曲线y=f(x)在点P(x,f(x))处切线的斜率。 000

2、导数应用:?过某点的切线不一定只有一条;(2)研究单调性步骤:分析

y=f(x)//定义域;求导数;解不等式f(x)?0得增区间;解不等式f(x)?0得减区间;注意/,,f(x),0f(x)f(x)=0的点;?求极值、最值步骤:求导数;求的根;检验在根左右