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=
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=
数学人气:495 ℃时间:2020-02-05 10:09:33
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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...答案还有52/5、148/5正弦函数在一、二和三、四象限函数值相等,ωπ/6+π/3<ωπ/4+π/3,当在一、二象限时,ωπ/6+π/3-2kπ=2kπ+π-(ωπ/4+π/3),ω=48k/5+4/5,ωπ/6+π/3-2kπ<π/2,ω<4k+2,k<1/4;当在三、四象限时,ωπ/6+π/3-(2kπ+π)=2kπ+2π-(ωπ/4+π/3),ω=48k/5+28/5,ωπ/6+π/3-(2kπ+π)<π/2,ω<12k+7,k>-7/12;综上k的取值范围:-7/12<k<1/4,因为k为整数,所以取k=0,ω=4/5或ω=28/5
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