Question

已知函数f(x)=Asin(ωx+ψ)(A>0,ω>0,|ψ|

Answer 1

∵当x=π/12时,f(x)取得最大值3 ∴A=3 ωπ/12+ψ=2kπ+π/2

∵当x=7π/12时,f(x)取得最小值-3 ∴ 7ωπ/12+ψ=2kπ+3π/2

两式相减：ωπ/2=π ω=2 ψ=π/3

∴ f(x)=3sin(2x+π/3)

h(x)=6sin(2x+π/3)+1-m 在x∈【-π/3,π/6】时有两个零点

h(-π/3)=6sin(-2π/3+π/3)+1-m=1-3√3 且 m>=1+3√3 且m