高一函数最值与单调性.pdf

新高一数学
函数最值与单调性
一、洞察万物
下列是一次函数 f(x)=x 和二次函数 f(x)=x2 的图象。
新高一数学
函数最值与单调性
一、洞察万物
下列是一次函数 f(x)=x 和二次函数 f(x)=x2 的图象。
一般地，设函数 y=f(x)的定义域为 I ,如果存在实数 M 满足：
（1）、
（2）、
那么，就称 M 是函数 y=f(x)的最大值。
求最大值应该注意的问题
1、 对于任意的 x 属于给定区间，都有 f(x)≤M 成立，“任意”是说对给
定区间的每一个值都必须满足不等式。
2、 最大值 M 必须是一个函数值，即它是值域中的一个元素。
````````````````````````````````````````````````````````````````````````````````````````````````````
````````````````````````````````````````````````````````````````````````````````````````````````````
````````````````````````````````````````````````````````````````````````````````````````````````````
- 1 -````````````````````````````````````````````````````````````````````````````````````````````````````
二、太阳出来了
1、函数 f(x)=x-2，x{0，1，2，4}的最大值为 。
2、函数 y=ax+1 在区间[1，3]上的最大值为 4，则 a= 。
2
3、已知函数 f(x)= （x[2，6]），求函数的最大值和最小值。
x 1
三、一锤定音
1、若函数 f(x)在区间（a，b）上是增函数，在区间（b，c）上也是增函数，则函数 f(x)