已知函数f(x)=sin(ωx+π/3),f(π/6)=f（π/4）,且f(x)在区间（π/6,π/4）有最小值无最大值,则ω=

Question

已知函数f(x)=sin(ωx+π/3),f(π/6)=f（π/4）,且f(x)在区间（π/6,π/4）有最小值无最大值,则ω=

Answer 1

f(π/6)=sin(ωπ/6+π/3),f(π/4)=sin(ωπ/4+π/3),sin(ωπ/6+π/3)=sin(ωπ/4+π/3),ωπ/6+π/3=ωπ/4+π/3,ωπ/6+π/3=π-ωπ/4-π/3,解得：ω=0,ω=4/5,取ω=4/5,f(x)在区间（π/6,π/4）有最大值无最小值.