已知函数f(x)=Msin(ωx+φ)(ω>0)的最大值是根号5,且在区间[kπ-π/6,kπ+π/3](k∈Z)上是增函数,在区间[kπ+π/3,kπ+5π/6](k∈Z)上是减函数,求函数f（x)

题目

已知函数f(x)=Msin(ωx+φ)(ω>0)的最大值是根号5,且在区间[kπ-π/6,kπ+π/3](k∈Z)上是增函数,在区间[kπ+π/3,kπ+5π/6](k∈Z)上是减函数,求函数f（x).

答案

M=根号5sinx在(2kπ-π/2,2kπ+π/2)上增在(2kπ+π/2,2kπ+3/2π)上减所以ωx+φ∈(2kπ-π/2,2kπ+π/2)时增,ωx+φ∈(2kπ+π/2,2kπ+3/2π)时减将x∈[kπ-π/6,kπ+π/3]上增,x∈[kπ+π/3,kπ+5π/6]减代入解得...