欢迎光临散文网 会员登陆 & 注册

先回到初始状态(2022全国甲11)

2022-11-27 15:41 作者:数学老顽童  | 我要投稿

(2022全国甲11)设函数f%5Cleft(%20x%20%5Cright)%20%3D%5Csin%20%5Cleft(%20%5Comega%20x%2B%5Cfrac%7B%5Cmathrm%7B%5Cpi%7D%7D%7B3%7D%20%5Cright)%20在区间%5Cleft(%200%2C%5Cmathrm%7B%5Cpi%7D%20%5Cright)%20恰有三个极值点、两个零点,则%5Comega%20的取值范围是(    )

A.%5Cleft%5B%20%5Cfrac%7B5%7D%7B3%7D%2C%5Cfrac%7B13%7D%7B6%7D%20%5Cright)%20

B.%5Cleft%5B%20%5Cfrac%7B5%7D%7B3%7D%2C%5Cfrac%7B19%7D%7B6%7D%20%5Cright)%20

C.%5Cleft(%20%5Cfrac%7B13%7D%7B6%7D%2C%5Cfrac%7B8%7D%7B3%7D%20%5Cright%5D%20

D.%5Cleft(%20%5Cfrac%7B13%7D%7B6%7D%2C%5Cfrac%7B19%7D%7B6%7D%20%5Cright%5D%20

解:(1)先令%5Comega%20%3D1,画出图象未伸缩之前的初始状态:

%5Comega%20%3C0,则伸缩后进入%5Cleft(%200%2C%5Cmathrm%7B%5Cpi%7D%20%5Cright)%20的极值点或零点全部由y侧提供,从y轴往数,依次是零点极值点零点极值点零点极值点,若要使伸缩后%5Cleft(%200%2C%5Cmathrm%7B%5Cpi%7D%20%5Cright)%20中有三个极值点,则必然也会有三个零点,不合题意;

%5Comega%20%3E0,则伸缩后进入%5Cleft(%200%2C%5Cmathrm%7B%5Cpi%7D%20%5Cright)%20的极值点或零点全部由y侧提供,从y轴往右数,第三个极值点为%5Cfrac%7B13%5Cpi%7D%7B6%7D%20,第三个零点为%5Cfrac%7B8%5Cpi%7D%7B3%7D%20,故%5Comega%20应满足

%5Cbegin%7Bcases%7D%09%5Cfrac%7B13%5Cmathrm%7B%5Cpi%7D%7D%7B6%7D%5Ccdot%20%5Cfrac%7B1%7D%7B%5Comega%7D%3C%5Cmathrm%7B%5Cpi%7D%2C%5C%5C%09%5Cfrac%7B8%5Cmathrm%7B%5Cpi%7D%7D%7B3%7D%5Ccdot%20%5Cfrac%7B1%7D%7B%5Comega%7D%5Cgeqslant%20%5Cmathrm%7B%5Cpi%7D.%5C%5C%5Cend%7Bcases%7D

解得%5Comega%5Cin%20%5Ccolor%7Bred%7D%7B%5Cleft(%20%5Cfrac%7B13%7D%7B6%7D%2C%5Cfrac%7B8%7D%7B3%7D%20%5Cright%5D%20%7D.

先回到初始状态(2022全国甲11)的评论 (共 条)

分享到微博请遵守国家法律