已知函数f(x)=sin(wx+π/3）（w>0),f(π/6）=f(π/3）,且f(x)在区间（π/6,π/3）有最小值,无最大值求w=

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已知函数f(x)=sin(wx+π/3）（w>0),f(π/6）=f(π/3）,且f(x)在区间（π/6,π/3）有最小值,无最大值求w=
已知函数f(x)=sin(wx+π/3）（w>0),f(π/6）=f(π/3）,且f(x)在区间（π/6,π/3）有最小值,无最大值
求w=

已知函数f(x)=sin(wx+π/3）（w>0),f(π/6）=f(π/3）,且f(x)在区间（π/6,π/3）有最小值,无最大值求w=
已知函数f(x)=sin(ωx+π/3）（ω>0),f(π/6）=f(π/3）,且f(x)在区间（π/6,π/3）有最小值,无最大值,求ω=?
(1/2)(π/6+π/3)=π/4,∵f(π/6）=f(π/3）,∴x=π/4是其对称轴,又因为f(x)有最小值-1,
故有f(π/4)=sin(ωπ/4+π/3)=-1,考虑到ω>0,故有ωπ/4+π/3=3π/2,ωπ/4=3π/2-π/3=7π/6,
∴ω=14/3.
事实上,f(π/6)=sin[(14/3)×(π/6)+π/3)]=sin(10π/9)=sin(π+π/9)=-sin(π/9)
f(π/3)=sin[(14/3)×(π/3)+π/3)]=sin(17π/9)=sin(2π-π/9)=-sin(π/9)=f(π/6)
f(π/4)=sin[(14/3)×(π/4)+π/3]=sin(9π/6)=sin(π+π/2)=-sin(π/2)=-1.
π/6

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