已知函数f(X)=根号2sin(wX一兀/4)(w>0)的最小正周期是兀.求w的值,若X已知函数f(X)=根号2sin(wX一兀/4)(w>0)的最小正周期是兀.求w的值、若X€[0,兀/2].且f(X)=0求X的值.求f(x)的单调区间.

问题描述:

已知函数f(X)=根号2sin(wX一兀/4)(w>0)的最小正周期是兀.求w的值,若X
已知函数f(X)=根号2sin(wX一兀/4)(w>0)的最小正周期是兀.求w的值、若X€[0,兀/2].且f(X)=0求X的值.求f(x)的单调区间.

T = 2π/w = π
所以w = 2
sin(2x - π/4) =0
2x - π/4 = 0
2x = π/4
x = π/8
(2) f(x) = 2sin(2x - π/4)
由f ‘ (x) = 2cos(2x - π/4) * 2 >0
得:cos(2x - π/4) >0
2kπ - π/2